The total surface area of a cylinder can be calculated by finding the sum of the areas of its two circular bases and the area of the curved surface (the lateral area). The formula for the total surface area (SA) is:
SA = 2πrh + 2πr²
Where:
- r is the radius of the cylinder's base
- h is the height of the cylinder
- π (pi) is approximately 3.14159
The first term (2πrh) represents the lateral surface area of the cylinder (the side), and the second term (2πr²) represents the combined area of the two circular bases. Adding these together gives you the total surface area of the cylinder.
1. What is the formula for the total surface of a cylinder?
11 answers
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.
To calculate the surface area of a cylinder with a radius (r) of 4 cm and a height (h) of 2 cm using the approximation 3.14 for π, you can use the formula:
SA = 2πrh + 2πr²
Plugging the values into the formula, you get:
SA = 2 * 3.14 * 4 cm * 2 cm + 2 * 3.14 * (4 cm)²
SA = 2 * 3.14 * 8 cm² + 2 * 3.14 * 16 cm²
SA = 50.24 cm² + 100.48 cm²
SA = 150.72 cm²
So, the surface area of the cylinder is 150.72 square centimeters.
SA = 2πrh + 2πr²
Plugging the values into the formula, you get:
SA = 2 * 3.14 * 4 cm * 2 cm + 2 * 3.14 * (4 cm)²
SA = 2 * 3.14 * 8 cm² + 2 * 3.14 * 16 cm²
SA = 50.24 cm² + 100.48 cm²
SA = 150.72 cm²
So, the surface area of the cylinder is 150.72 square centimeters.
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.
To find the surface area of a cylinder, we first need to find the radius, which is half of the diameter. Since the diameter is given as 12 inches, the radius (r) is:
r = diameter / 2
r = 12 inches / 2
r = 6 inches
Now, we have the height (h) of 10 inches and the radius of 6 inches. We use the formula for the surface area (SA) of a cylinder:
SA = 2πrh + 2πr²
Using 3.14 for π, we substitute the values of r and h into the formula:
SA = 2 * 3.14 * 6 inches * 10 inches + 2 * 3.14 * (6 inches)²
SA = 2 * 3.14 * 60 inches² + 2 * 3.14 * 36 inches²
SA = 376.8 inches² + 226.08 inches²
SA = 602.88 inches²
So, the surface area of the cylinder is 602.88 square inches.
r = diameter / 2
r = 12 inches / 2
r = 6 inches
Now, we have the height (h) of 10 inches and the radius of 6 inches. We use the formula for the surface area (SA) of a cylinder:
SA = 2πrh + 2πr²
Using 3.14 for π, we substitute the values of r and h into the formula:
SA = 2 * 3.14 * 6 inches * 10 inches + 2 * 3.14 * (6 inches)²
SA = 2 * 3.14 * 60 inches² + 2 * 3.14 * 36 inches²
SA = 376.8 inches² + 226.08 inches²
SA = 602.88 inches²
So, the surface area of the cylinder 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 of 7 inches. How many square inches of icing will be needed to cover the sides and top of the cake? Icing will
To cover the sides and top of the cylinder cake with icing, the baker needs to calculate the lateral (side) surface area and the area of the top circle. The bottom does not need icing because it's typically placed on a surface or a cake board. So, we'll calculate the lateral surface area plus the area of just one base (the top).
The lateral surface area (side) is calculated by finding the circumference of the top of the cake (which is the same as the bottom) and multiplying it by the height. The formula for lateral surface area is:
Lateral Surface Area = 2πrh
Where:
- r is the radius of the cylinder's base
- h is the height of the cylinder
- π (pi) is approximately 3.14159, but we will use 3.14 as the approximation
Given:
r = 5 inches
h = 7 inches
Lateral Surface Area = 2 * 3.14 * 5 inches * 7 inches
Lateral Surface Area = 2 * 3.14 * 35 inches²
Lateral Surface Area = 219.8 inches²
The area of the top of the cake, which is a circle, is calculated by the formula:
Area of Circle = πr²
Area of Circle = 3.14 * (5 inches)²
Area of Circle = 3.14 * 25 inches²
Area of Circle = 78.5 inches²
Now to find the total amount of icing needed, you add the lateral surface area to the area of the top:
Total Surface Area for Icing = Lateral Surface Area + Area of Circle
Total Surface Area for Icing = 219.8 inches² + 78.5 inches²
Total Surface Area for Icing = 298.3 inches²
So, the baker will need 298.3 square inches of icing to cover the sides and top of the cake.
The lateral surface area (side) is calculated by finding the circumference of the top of the cake (which is the same as the bottom) and multiplying it by the height. The formula for lateral surface area is:
Lateral Surface Area = 2πrh
Where:
- r is the radius of the cylinder's base
- h is the height of the cylinder
- π (pi) is approximately 3.14159, but we will use 3.14 as the approximation
Given:
r = 5 inches
h = 7 inches
Lateral Surface Area = 2 * 3.14 * 5 inches * 7 inches
Lateral Surface Area = 2 * 3.14 * 35 inches²
Lateral Surface Area = 219.8 inches²
The area of the top of the cake, which is a circle, is calculated by the formula:
Area of Circle = πr²
Area of Circle = 3.14 * (5 inches)²
Area of Circle = 3.14 * 25 inches²
Area of Circle = 78.5 inches²
Now to find the total amount of icing needed, you add the lateral surface area to the area of the top:
Total Surface Area for Icing = Lateral Surface Area + Area of Circle
Total Surface Area for Icing = 219.8 inches² + 78.5 inches²
Total Surface Area for Icing = 298.3 inches²
So, 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
If the farmer needs to refinish only the side of the silo and not the top or bottom, then we only need to calculate the lateral surface area (the area of the side) of the cylindrical silo.
The formula for the lateral surface area (LSA) of a cylinder is:
LSA = 2πrh
Where:
- r is the radius of the cylinder's base
- h is the height of the cylinder
- π (pi) is approximately 3.14159
Given:
r = 4 feet
h = 30 feet
Using these values, we can calculate the lateral surface area:
LSA = 2 * π * 4 feet * 30 feet
LSA = 2 * 3.14159 * 4 feet * 30 feet
Now, let's do the calculation:
LSA = 2 * 3.14159 * 120 feet²
LSA = 6.28318 * 120 feet²
LSA = 753.982 square feet
Therefore, the farmer needs approximately 753.982 square feet of aluminum to refinish the side of the silo. This value can be rounded as necessary, depending on the precision required for the material purchase; for practical purposes, it might be rounded up to ensure there's a slight excess to account for any waste or cutting overlap.
The formula for the lateral surface area (LSA) of a cylinder is:
LSA = 2πrh
Where:
- r is the radius of the cylinder's base
- h is the height of the cylinder
- π (pi) is approximately 3.14159
Given:
r = 4 feet
h = 30 feet
Using these values, we can calculate the lateral surface area:
LSA = 2 * π * 4 feet * 30 feet
LSA = 2 * 3.14159 * 4 feet * 30 feet
Now, let's do the calculation:
LSA = 2 * 3.14159 * 120 feet²
LSA = 6.28318 * 120 feet²
LSA = 753.982 square feet
Therefore, the farmer needs approximately 753.982 square feet of aluminum to refinish the side of the silo. This value can be rounded as necessary, depending on the precision required for the material purchase; for practical purposes, it might be rounded up to ensure there's a slight excess to account for any waste or cutting overlap.
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 calculate the amount of aluminum needed to refinish the side of the silo, we need to find the lateral surface area (the side area) of the cylinder. The farmer does not need to refinish the top or bottom, so we'll only calculate the side.
The lateral surface area (LSA) is given by the formula:
LSA = 2πrh
Where:
- r is the radius of the silo
- h is the height of the silo
- π (pi) is approximately 3.14159, but we'll use 3.14 as stated
Let's plug in the given values (r = 4 feet and h = 30 feet) into the formula:
LSA = 2 * 3.14 * 4 feet * 30 feet
Now, perform the multiplication:
LSA = 2 * 3.14 * 120 feet²
LSA = 6.28 * 120 feet²
LSA = 753.6 square feet
Rounded to the nearest tenth, the farmer needs 753.6 square feet of aluminum to refinish the side of the silo.
The lateral surface area (LSA) is given by the formula:
LSA = 2πrh
Where:
- r is the radius of the silo
- h is the height of the silo
- π (pi) is approximately 3.14159, but we'll use 3.14 as stated
Let's plug in the given values (r = 4 feet and h = 30 feet) into the formula:
LSA = 2 * 3.14 * 4 feet * 30 feet
Now, perform the multiplication:
LSA = 2 * 3.14 * 120 feet²
LSA = 6.28 * 120 feet²
LSA = 753.6 square feet
Rounded to the nearest tenth, the farmer needs 753.6 square feet of aluminum to refinish the side of the silo.
1 answer