To find the surface area of a cylinder, you need to calculate the area of the two circular bases and the area of the curved surface (the lateral area).
The area of one circular base is given by the formula A = πr², where r is the radius. Since the cylinder has two bases, you multiply the area of one base by 2.
Given r = 4 cm, the area of one base is:
A_base = πr² = 3.14 * (4 cm)² = 3.14 * 16 cm² = 50.24 cm²
The area of two bases is:
2 * A_base = 2 * 50.24 cm² = 100.48 cm²
The lateral surface area of a cylinder is given by the formula A_lateral = 2πrh, where h is the height.
Given h = 2 cm, the lateral surface area is:
A_lateral = 2πrh = 2 * 3.14 * 4 cm * 2 cm = 50.24 cm²
Now, add the area of the two bases to the lateral surface area to get the total surface area:
Surface Area_total = Area_bases + A_lateral = 100.48 cm² + 50.24 cm² = 150.72 cm²
So, the surface area of the cylinder is 150.72 cm².
find the surface area of a cylinder with a radius of 4 cm and a height of 2 cm. use the approximation of 3.14 for pi
19 answers
what is the formula for the total surface area of a cylinder?
The formula for the total surface area of a cylinder is given by the sum of the areas of the circular bases and the lateral area (the area of the side). The formula is:
Total Surface Area (A_total) = 2 * Area of Base + Lateral Surface Area
Total Surface Area (A_total) = 2πr² + 2πrh
Where:
- π (Pi) is the constant approximately equal to 3.14.
- r is the radius of the circular base of the cylinder.
- h is the height of the cylinder.
Intuitively, the first term (2πr²) represents the area of the top and bottom circles, and the second term (2πrh) represents the area of the side of the cylinder when it is unwrapped into a rectangle.
Total Surface Area (A_total) = 2 * Area of Base + Lateral Surface Area
Total Surface Area (A_total) = 2πr² + 2πrh
Where:
- π (Pi) is the constant approximately equal to 3.14.
- r is the radius of the circular base of the cylinder.
- h is the height of the cylinder.
Intuitively, the first term (2πr²) represents the area of the top and bottom circles, and the second term (2πrh) represents the area of the side of the cylinder when it is unwrapped into a rectangle.
find the surface area of a cylinder with a diameter of 12 inches and height of 10 inches. use the approximation of 3.14 for pi
First, let's find the radius of the cylinder, which is half of the diameter. The diameter is 12 inches, so the radius (r) is 12 inches / 2 = 6 inches.
Now, we'll use the formula for the total surface area of a cylinder:
Total Surface Area (A_total) = 2πr² + 2πrh
Let's plug in the values:
r = 6 inches
h = 10 inches
π ≈ 3.14
Total Surface Area (A_total) = 2 * 3.14 * (6 inches)² + 2 * 3.14 * 6 inches * 10 inches
First, we calculate the area of the top and bottom circles (2πr²):
Circle Area = πr² = 3.14 * (6 inches)² = 3.14 * 36 inches² = 113.04 inches²
Since there are two bases (top and bottom):
2 * Circle Area = 2 * 113.04 inches² = 226.08 inches²
Now, we calculate the lateral surface area (2πrh):
Lateral Surface Area = 2 * π * r * h = 2 * 3.14 * 6 inches * 10 inches = 376.8 inches²
Finally, we sum both areas to get the total surface area:
Total Surface Area (A_total) = 226.08 inches² + 376.8 inches² = 602.88 inches²
The surface area of the cylinder with a diameter of 12 inches and a height of 10 inches, using π ≈ 3.14, is 602.88 square inches.
Now, we'll use the formula for the total surface area of a cylinder:
Total Surface Area (A_total) = 2πr² + 2πrh
Let's plug in the values:
r = 6 inches
h = 10 inches
π ≈ 3.14
Total Surface Area (A_total) = 2 * 3.14 * (6 inches)² + 2 * 3.14 * 6 inches * 10 inches
First, we calculate the area of the top and bottom circles (2πr²):
Circle Area = πr² = 3.14 * (6 inches)² = 3.14 * 36 inches² = 113.04 inches²
Since there are two bases (top and bottom):
2 * Circle Area = 2 * 113.04 inches² = 226.08 inches²
Now, we calculate the lateral surface area (2πrh):
Lateral Surface Area = 2 * π * r * h = 2 * 3.14 * 6 inches * 10 inches = 376.8 inches²
Finally, we sum both areas to get the total surface area:
Total Surface Area (A_total) = 226.08 inches² + 376.8 inches² = 602.88 inches²
The surface area of the cylinder with a diameter of 12 inches and a height of 10 inches, using π ≈ 3.14, is 602.88 square inches.
a baker needs to cover a cylinder cake with icing. the cake has a radius of 5 inches and a height 7 inches. how many square inches of icing will be needed to cover the sides and top of the cake? icing will not be added to the bottom of the cake. use 3.14 for pi and round your answer to the nearest tenth
To cover the cake with icing, the baker needs to calculate the surface area of the sides (lateral surface area) and the top of the cylinder cake. The bottom does not need icing.
We can use the formulas for the areas of the circular top and the lateral surface:
Top Area (A_top) = πr²
Lateral Surface Area (A_lateral) = 2πrh
Where:
π (Pi) is approximately 3.14,
r is the radius of the cylinder cake, which is 5 inches,
h is the height of the cylinder cake, which is 7 inches.
Let's start by calculating the area of the top:
A_top = πr² = 3.14 * (5 inches)² = 3.14 * 25 inches² = 78.5 inches²
Now, we calculate the lateral surface area:
A_lateral = 2πrh = 2 * 3.14 * 5 inches * 7 inches = 2 * 3.14 * 35 inches² = 219.8 inches²
The total amount of icing needed is the sum of the top area and the lateral surface area:
Total Icing Area = A_top + A_lateral = 78.5 inches² + 219.8 inches² = 298.3 inches²
Rounding to the nearest tenth, the baker will need 298.3 square inches of icing to cover the sides and top of the cake.
We can use the formulas for the areas of the circular top and the lateral surface:
Top Area (A_top) = πr²
Lateral Surface Area (A_lateral) = 2πrh
Where:
π (Pi) is approximately 3.14,
r is the radius of the cylinder cake, which is 5 inches,
h is the height of the cylinder cake, which is 7 inches.
Let's start by calculating the area of the top:
A_top = πr² = 3.14 * (5 inches)² = 3.14 * 25 inches² = 78.5 inches²
Now, we calculate the lateral surface area:
A_lateral = 2πrh = 2 * 3.14 * 5 inches * 7 inches = 2 * 3.14 * 35 inches² = 219.8 inches²
The total amount of icing needed is the sum of the top area and the lateral surface area:
Total Icing Area = A_top + A_lateral = 78.5 inches² + 219.8 inches² = 298.3 inches²
Rounding to the nearest tenth, the baker will need 298.3 square inches of icing to cover the sides and top of the cake.
a silo is a large cylinder container that holds hay. A farmer needs to refinish the side of the silo with aluminum. the silo has a radius of 4 feet and a height of 30 feet. how many square feet of aluminum does the farmer need to refinish the silo? he will not be refinishing the top or bottom of the silo. use 3.14 for pi and round your answer to the nearest tenth
To refinish the side of the silo, the farmer needs to calculate the lateral surface area of the cylinder, as the top and bottom are not being refinished.
The formula for the lateral surface area (A_lateral) of a cylinder is given by:
A_lateral = 2πrh
Where:
- π (Pi) is approximately 3.14,
- r is the radius of the cylinder,
- h is the height of the cylinder.
Given the radius (r) of 4 feet and the height (h) of 30 feet, we can calculate the lateral surface area as follows:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 4 feet * 30 feet
A_lateral = 2 * 3.14 * 120 feet²
A_lateral = 2 * 376.8 feet²
A_lateral = 753.6 feet²
Rounding to the nearest tenth, the farmer will need 753.6 square feet of aluminum to refinish the side of the silo.
The formula for the lateral surface area (A_lateral) of a cylinder is given by:
A_lateral = 2πrh
Where:
- π (Pi) is approximately 3.14,
- r is the radius of the cylinder,
- h is the height of the cylinder.
Given the radius (r) of 4 feet and the height (h) of 30 feet, we can calculate the lateral surface area as follows:
A_lateral = 2 * π * r * h
A_lateral = 2 * 3.14 * 4 feet * 30 feet
A_lateral = 2 * 3.14 * 120 feet²
A_lateral = 2 * 376.8 feet²
A_lateral = 753.6 feet²
Rounding to the nearest tenth, the farmer will need 753.6 square feet of aluminum to refinish the side of the silo.
find the surface area of a cylinder with a radius of 5 and a height of 10 inches. use the approximation 3.14 for pi
The surface area of a cylinder is the sum of the areas of the two circular ends (bases) plus the area of the side (the lateral surface area).
The formula for the surface area of a cylinder is:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height.
Using the values \( r = 5 \) inches and \( h = 10 \) inches, the surface area can be calculated as follows:
First, we calculate the area of the two circular bases:
\[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (5 \text{ inches})^2 = 2 \times 3.14 \times 25 \text{ inches}^2 = 2 \times 78.5 \text{ inches}^2 = 157 \text{ inches}^2 \]
Next, we calculate the lateral surface area:
\[ \text{Lateral surface area} = 2\pi rh = 2 \times 3.14 \times 5 \text{ inches} \times 10 \text{ inches} = 2 \times 3.14 \times 50 \text{ inches}^2 = 314 \text{ inches}^2 \]
Now, we add the two areas together to get the total surface area:
\[ \text{Total surface area} = 157 \text{ inches}^2 + 314 \text{ inches}^2 = 471 \text{ inches}^2 \]
So, the surface area of the cylinder with a radius of 5 inches and a height of 10 inches, using 3.14 for pi, is 471 square inches.
The formula for the surface area of a cylinder is:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height.
Using the values \( r = 5 \) inches and \( h = 10 \) inches, the surface area can be calculated as follows:
First, we calculate the area of the two circular bases:
\[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (5 \text{ inches})^2 = 2 \times 3.14 \times 25 \text{ inches}^2 = 2 \times 78.5 \text{ inches}^2 = 157 \text{ inches}^2 \]
Next, we calculate the lateral surface area:
\[ \text{Lateral surface area} = 2\pi rh = 2 \times 3.14 \times 5 \text{ inches} \times 10 \text{ inches} = 2 \times 3.14 \times 50 \text{ inches}^2 = 314 \text{ inches}^2 \]
Now, we add the two areas together to get the total surface area:
\[ \text{Total surface area} = 157 \text{ inches}^2 + 314 \text{ inches}^2 = 471 \text{ inches}^2 \]
So, the surface area of the cylinder with a radius of 5 inches and a height of 10 inches, using 3.14 for pi, is 471 square inches.
find the surface area of the cylinder. use the approximation 3.14 for pi.
(diameter 7 yd.)
(height 8 yrd.)
(diameter 7 yd.)
(height 8 yrd.)
To find the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2 \pi r^2 + 2 \pi r h \]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14. The diameter is given, so the radius is half of the diameter.
First, we find the radius by dividing the diameter by 2:
\[ \text{Diameter} = 7 \text{ yd} \]
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{7 \text{ yd}}{2} = 3.5 \text{ yd} \]
Now we can calculate the surface area using the given height of 8 yd:
The area of the two circular ends (bases) is:
\[ \text{Area of bases} (A_b) = 2 \pi r^2 = 2 \times 3.14 \times (3.5 \text{ yd})^2 \]
\[ A_b = 2 \times 3.14 \times 12.25 \text{ yd}^2 \]
\[ A_b = 2 \times 3.14 \times 12.25 \text{ yd}^2 = 2 \times 38.465 \text{ yd}^2 = 76.93 \text{ yd}^2 \]
The lateral surface area is:
\[ \text{Lateral surface area} (A_l) = 2 \pi r h = 2 \times 3.14 \times 3.5 \text{ yd} \times 8 \text{ yd} \]
\[ A_l = 2 \times 3.14 \times 28 \text{ yd}^2 = 175.84 \text{ yd}^2 \]
Adding both areas together, we get the total surface area:
\[ \text{Total surface area} = A_b + A_l = 76.93 \text{ yd}^2 + 175.84 \text{ yd}^2 \]
\[ \text{Total surface area} = 252.77 \text{ yd}^2 \]
So, the surface area of the cylinder with a diameter of 7 yards and a height of 8 yards, using 3.14 for pi, is approximately 252.77 square yards.
\[ \text{Surface Area} = 2 \pi r^2 + 2 \pi r h \]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14. The diameter is given, so the radius is half of the diameter.
First, we find the radius by dividing the diameter by 2:
\[ \text{Diameter} = 7 \text{ yd} \]
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{7 \text{ yd}}{2} = 3.5 \text{ yd} \]
Now we can calculate the surface area using the given height of 8 yd:
The area of the two circular ends (bases) is:
\[ \text{Area of bases} (A_b) = 2 \pi r^2 = 2 \times 3.14 \times (3.5 \text{ yd})^2 \]
\[ A_b = 2 \times 3.14 \times 12.25 \text{ yd}^2 \]
\[ A_b = 2 \times 3.14 \times 12.25 \text{ yd}^2 = 2 \times 38.465 \text{ yd}^2 = 76.93 \text{ yd}^2 \]
The lateral surface area is:
\[ \text{Lateral surface area} (A_l) = 2 \pi r h = 2 \times 3.14 \times 3.5 \text{ yd} \times 8 \text{ yd} \]
\[ A_l = 2 \times 3.14 \times 28 \text{ yd}^2 = 175.84 \text{ yd}^2 \]
Adding both areas together, we get the total surface area:
\[ \text{Total surface area} = A_b + A_l = 76.93 \text{ yd}^2 + 175.84 \text{ yd}^2 \]
\[ \text{Total surface area} = 252.77 \text{ yd}^2 \]
So, the surface area of the cylinder with a diameter of 7 yards and a height of 8 yards, using 3.14 for pi, is approximately 252.77 square yards.
find the surface area of the cylinder. use the approximation 3.14 for pi.
(diameter 2 yd.)
(height 3 yd.)
(diameter 2 yd.)
(height 3 yd.)
To find the surface area of the cylinder, we will use the formula for the surface area of a cylinder and substitute the given values for the radius and height. The only complication here is that we are provided with the diameter, not the radius. The radius is half the diameter, so we first calculate the radius:
\[ \text{Radius} (r) = \text{Diameter} / 2 = 2 \text{ yd} / 2 = 1 \text{ yd} \]
Now, we have the radius \( r = 1 \text{ yd} \) and the height \( h = 3 \text{ yd} \). We can find the surface area using the formula, which includes the areas of the two circular ends and the lateral surface area:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Substituting the values for \( \pi, r, \) and \( h \):
\[ \text{Surface Area} = 2 \times 3.14 \times (1 \text{ yd})^2 + 2 \times 3.14 \times 1 \text{ yd} \times 3 \text{ yd} \]
\[ \text{Surface Area} = 2 \times 3.14 \times 1 \text{ yd}^2 + 6.28 \times 3 \text{ yd} \]
\[ \text{Surface Area} = 6.28 \text{ yd}^2 + 18.84 \text{ yd}^2 \]
\[ \text{Surface Area} = 25.12 \text{ yd}^2 \]
Therefore, the surface area of the cylinder with a diameter of 2 yards and a height of 3 yards, using 3.14 for pi, is approximately 25.12 square yards.
\[ \text{Radius} (r) = \text{Diameter} / 2 = 2 \text{ yd} / 2 = 1 \text{ yd} \]
Now, we have the radius \( r = 1 \text{ yd} \) and the height \( h = 3 \text{ yd} \). We can find the surface area using the formula, which includes the areas of the two circular ends and the lateral surface area:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Substituting the values for \( \pi, r, \) and \( h \):
\[ \text{Surface Area} = 2 \times 3.14 \times (1 \text{ yd})^2 + 2 \times 3.14 \times 1 \text{ yd} \times 3 \text{ yd} \]
\[ \text{Surface Area} = 2 \times 3.14 \times 1 \text{ yd}^2 + 6.28 \times 3 \text{ yd} \]
\[ \text{Surface Area} = 6.28 \text{ yd}^2 + 18.84 \text{ yd}^2 \]
\[ \text{Surface Area} = 25.12 \text{ yd}^2 \]
Therefore, the surface area of the cylinder with a diameter of 2 yards and a height of 3 yards, using 3.14 for pi, is approximately 25.12 square yards.
a can of olives has a diameter of 6 inches and a height of 4 inches. how many square inches of paper will be needed for the label on the outside of the can? use 3.14 for pi
To create a label for the outside of a can of olives, you only need to cover the lateral surface area. This area is like a rectangle when the label is unwrapped, where the width of the rectangle is the circumference of the can and the height is the same as the can.
The formula for the lateral surface area (A_lateral) is:
\[ A_lateral = 2 \pi r h \]
Where \( \pi \) is approximately 3.14, \( r \) is the radius of the cylinder, and \( h \) is the height of the cylinder.
First, we find the radius by dividing the diameter in half:
\[ \text{Diameter} = 6 \text{ inches} \]
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{6 \text{ inches}}{2} = 3 \text{ inches} \]
Using the given height \( h = 4 \text{ inches} \), we can calculate the lateral surface area:
\[ A_lateral = 2 \times \pi \times r \times h \]
\[ A_lateral = 2 \times 3.14 \times 3 \text{ inches} \times 4 \text{ inches} \]
\[ A_lateral = 2 \times 3.14 \times 12 \text{ inches}^2 \]
\[ A_lateral = 6.28 \times 12 \text{ inches}^2 \]
\[ A_lateral = 75.36 \text{ inches}^2 \]
Therefore, 75.36 square inches of paper will be needed for the label on the outside of the can. Since the result should be in square inches and not include fractions of a square inch, we don't need to round this calculation to the nearest tenth.
The formula for the lateral surface area (A_lateral) is:
\[ A_lateral = 2 \pi r h \]
Where \( \pi \) is approximately 3.14, \( r \) is the radius of the cylinder, and \( h \) is the height of the cylinder.
First, we find the radius by dividing the diameter in half:
\[ \text{Diameter} = 6 \text{ inches} \]
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{6 \text{ inches}}{2} = 3 \text{ inches} \]
Using the given height \( h = 4 \text{ inches} \), we can calculate the lateral surface area:
\[ A_lateral = 2 \times \pi \times r \times h \]
\[ A_lateral = 2 \times 3.14 \times 3 \text{ inches} \times 4 \text{ inches} \]
\[ A_lateral = 2 \times 3.14 \times 12 \text{ inches}^2 \]
\[ A_lateral = 6.28 \times 12 \text{ inches}^2 \]
\[ A_lateral = 75.36 \text{ inches}^2 \]
Therefore, 75.36 square inches of paper will be needed for the label on the outside of the can. Since the result should be in square inches and not include fractions of a square inch, we don't need to round this calculation to the nearest tenth.
a wheel of cheese has a diameter of 6 inches and a height of 2 inch. a chef is making a appetizer where the cheese will be covered with pastry. to know how much pastry needed, the chef wants to know the surface area of the cheese wheel. what is the total surface area of the cheese wheel in sq inches? use 3.14 for pi
To find the total surface area of the cheese wheel, you'll need to calculate the area of the top and bottom circular faces as well as the lateral surface area.
The formula for the surface area of a cylinder is:
\[ \text{Total Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( \pi \) is approximately 3.14,
- \( r \) is the radius,
- \( h \) is the height.
Since the diameter of the cheese wheel is 6 inches, the radius \( r \) is:
\[ r = \text{Diameter}/2 = 6 \text{ inches}/2 = 3 \text{ inches} \]
Now, given the height \( h = 2 \text{ inches} \), you can calculate the total surface area.
First, calculate the area of both circular faces:
\[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (3 \text{ inches})^2 \]
\[ \text{Area of bases} = 2 \times 3.14 \times 9 \text{ inches}^2 = 56.52 \text{ inches}^2 \]
Next, calculate the lateral surface area:
\[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 3 \text{ inches} \times 2 \text{ inches} \]
\[ \text{Lateral Surface Area} = 6.28 \times 3 \text{ inches} \times 2 \text{ inches} \]
\[ \text{Lateral Surface Area} = 37.68 \text{ inches}^2 \]
Now, add the areas together to get the total surface area:
\[ \text{Total Surface Area} = \text{Area of bases} + \text{Lateral Surface Area} \]
\[ \text{Total Surface Area} = 56.52 \text{ inches}^2 + 37.68 \text{ inches}^2 \]
\[ \text{Total Surface Area} = 94.2 \text{ inches}^2 \]
Therefore, the total surface area of the cheese wheel is approximately 94.2 square inches.
The formula for the surface area of a cylinder is:
\[ \text{Total Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( \pi \) is approximately 3.14,
- \( r \) is the radius,
- \( h \) is the height.
Since the diameter of the cheese wheel is 6 inches, the radius \( r \) is:
\[ r = \text{Diameter}/2 = 6 \text{ inches}/2 = 3 \text{ inches} \]
Now, given the height \( h = 2 \text{ inches} \), you can calculate the total surface area.
First, calculate the area of both circular faces:
\[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (3 \text{ inches})^2 \]
\[ \text{Area of bases} = 2 \times 3.14 \times 9 \text{ inches}^2 = 56.52 \text{ inches}^2 \]
Next, calculate the lateral surface area:
\[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 3 \text{ inches} \times 2 \text{ inches} \]
\[ \text{Lateral Surface Area} = 6.28 \times 3 \text{ inches} \times 2 \text{ inches} \]
\[ \text{Lateral Surface Area} = 37.68 \text{ inches}^2 \]
Now, add the areas together to get the total surface area:
\[ \text{Total Surface Area} = \text{Area of bases} + \text{Lateral Surface Area} \]
\[ \text{Total Surface Area} = 56.52 \text{ inches}^2 + 37.68 \text{ inches}^2 \]
\[ \text{Total Surface Area} = 94.2 \text{ inches}^2 \]
Therefore, the total surface area of the cheese wheel is approximately 94.2 square inches.
9 answers