To find the surface area of the net diagram of the right circular cylinder, we need to calculate the areas of the three different surfaces: the lateral surface area and the two circular bases.
1. Lateral Surface Area:
The lateral surface area of a cylinder can be calculated by multiplying the height of the cylinder by the circumference of the base circle. In this case, the height of the cylinder is 4 inches and the radius of the base circle is 8 inches.
Lateral Surface Area = height x circumference of base
Lateral Surface Area = 4 x 2 x π x radius
Lateral Surface Area = 4 x 2 x 3.14 x 8
Lateral Surface Area = 200.96 square inches
2. Circular Base Areas:
The area of a circle can be calculated by using the formula A = πr^2, where r is the radius of the circle. In this case, the radius of the base circles is 8 inches.
Base Area = πr^2
Base Area = 3.14 x 8^2
Base Area = 3.14 x 64
Base Area = 200.96 square inches
3. Total Surface Area:
Now, to find the total surface area of the net diagram of the right circular cylinder, we need to add the lateral surface area and the two circular base areas together.
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 200.96 + 2(200.96)
Total Surface Area = 200.96 + 401.92
Total Surface Area = 602.88 square inches
Therefore, the surface area of the net diagram of the right circular cylinder is 602.88 square inches.
An illustration shows a horizontal rectangle of height 4 inches with a circle of radius 8 inches attached to its top left and a circle of radius 8 inches attached to its bottom right
Find the surface area of the net diagram of the right circular cylinder. Use 3.14 for π .
13 answers
That's right! Question 2:
An illustration shows a horizontal rectangle of height 9 inches with a circle of radius 10 inches attached to its top left and a circle of radius 10 inches attached to its bottom right.
Find the surface area of the net diagram of the right circular cylinder. Use 3.14 for π .
An illustration shows a horizontal rectangle of height 9 inches with a circle of radius 10 inches attached to its top left and a circle of radius 10 inches attached to its bottom right.
Find the surface area of the net diagram of the right circular cylinder. Use 3.14 for π .
To find the surface area of the net diagram of the right circular cylinder given these dimensions, we need to calculate the areas of the lateral surface, and the two circular bases.
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by the formula: Lateral Surface Area = height x circumference of base
In this case, the height of the cylinder is 9 inches and the radius of the base circle is 10 inches.
Lateral Surface Area = 9 x 2πr
Lateral Surface Area = 9 x 2 x 3.14 x 10
Lateral Surface Area = 565.2 square inches
2. Circular Base Areas:
The area of a circle is given by the formula: A = πr^2
In this case, the radius of the base circle is 10 inches.
Base Area = πr^2
Base Area = 3.14 x 10^2
Base Area = 3.14 x 100
Base Area = 314 square inches
3. Total Surface Area:
The total surface area of the net diagram of the right circular cylinder is the sum of the lateral surface area and the two circular base areas.
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 565.2 + 2(314)
Total Surface Area = 565.2 + 628
Total Surface Area = 1193.2 square inches
Therefore, the surface area of the net diagram of the right circular cylinder with the given dimensions is 1193.2 square inches.
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by the formula: Lateral Surface Area = height x circumference of base
In this case, the height of the cylinder is 9 inches and the radius of the base circle is 10 inches.
Lateral Surface Area = 9 x 2πr
Lateral Surface Area = 9 x 2 x 3.14 x 10
Lateral Surface Area = 565.2 square inches
2. Circular Base Areas:
The area of a circle is given by the formula: A = πr^2
In this case, the radius of the base circle is 10 inches.
Base Area = πr^2
Base Area = 3.14 x 10^2
Base Area = 3.14 x 100
Base Area = 314 square inches
3. Total Surface Area:
The total surface area of the net diagram of the right circular cylinder is the sum of the lateral surface area and the two circular base areas.
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 565.2 + 2(314)
Total Surface Area = 565.2 + 628
Total Surface Area = 1193.2 square inches
Therefore, the surface area of the net diagram of the right circular cylinder with the given dimensions is 1193.2 square inches.
Correct! Question 3:
An illustration shows a rectangle of unknown height with a circle of radius 3 feet attached to its top left and a circle of radius 3 feet attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 395.64 feet2 , find the height of the net diagram. Use 3.14 for π .
An illustration shows a rectangle of unknown height with a circle of radius 3 feet attached to its top left and a circle of radius 3 feet attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 395.64 feet2 , find the height of the net diagram. Use 3.14 for π .
To determine the height of the rectangle in the net diagram of the right circular cylinder based on the given surface area, we will first calculate the lateral surface area of the cylinder and then use it to find the height.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by Lateral Surface Area = height x circumference of the base.
The circumference of the base can be calculated using the formula 2πr, where r is the radius.
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
Now, we can calculate the height of the net diagram by rearranging the formula for lateral surface area:
Lateral Surface Area = height x Circumference
395.64 = height x 18.84
height = 395.64 / 18.84
height = 20.98 feet
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 20.98 feet.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by Lateral Surface Area = height x circumference of the base.
The circumference of the base can be calculated using the formula 2πr, where r is the radius.
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
Now, we can calculate the height of the net diagram by rearranging the formula for lateral surface area:
Lateral Surface Area = height x Circumference
395.64 = height x 18.84
height = 395.64 / 18.84
height = 20.98 feet
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 20.98 feet.
Nope, choose a different answer!
Let's try solving it using another method.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
The lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of base
The circumference of the base can be calculated using the formula 2πr, where r is the radius:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
Given that the lateral surface area is 395.64 feet², we can set up an equation using the formula for lateral surface area:
395.64 = height * 18.84
Solving for height:
height = 395.64 / 18.84
height ≈ 20.98 feet
Therefore, the height of the net diagram of the right circular cylinder is approximately 20.98 feet.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
The lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of base
The circumference of the base can be calculated using the formula 2πr, where r is the radius:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
Given that the lateral surface area is 395.64 feet², we can set up an equation using the formula for lateral surface area:
395.64 = height * 18.84
Solving for height:
height = 395.64 / 18.84
height ≈ 20.98 feet
Therefore, the height of the net diagram of the right circular cylinder is approximately 20.98 feet.
Still no.
Let's try solving it using a different approach.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
We know that the lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given the lateral surface area as 395.64 feet². We can now set up an equation to find the height:
395.64 = height * 18.84
height = 395.64 / 18.84
height ≈ 21 feet
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 21 feet.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
We know that the lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given the lateral surface area as 395.64 feet². We can now set up an equation to find the height:
395.64 = height * 18.84
height = 395.64 / 18.84
height ≈ 21 feet
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 21 feet.
It's NOT 20.98 or 21.
Let's try to solve it again.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
The lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of the base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given that the lateral surface area is 395.64 feet². Let's find the height using this information.
395.64 = height * 18.84
height = 395.64 / 18.84
height = 21 feet
Therefore, the height of the net diagram of the right circular cylinder is 21 feet.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
The lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of the base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given that the lateral surface area is 395.64 feet². Let's find the height using this information.
395.64 = height * 18.84
height = 395.64 / 18.84
height = 21 feet
Therefore, the height of the net diagram of the right circular cylinder is 21 feet.
An illustration shows a rectangle of unknown height with a circle of radius 3 feet attached to its top left and a circle of radius 3 feet attached to its bottom right.
If the surface area of the net diagram of the right circular cylinder is 395.64 feet2 , find the height of the net diagram. Use 3.14 for π .
The answer is NOT 20.98 or 21.
If the surface area of the net diagram of the right circular cylinder is 395.64 feet2 , find the height of the net diagram. Use 3.14 for π .
The answer is NOT 20.98 or 21.
Let's approach this problem with a different perspective.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
We know that the lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of the base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given the lateral surface area as 395.64 feet². The lateral surface area can also be calculated using the formula:
Lateral Surface Area = 2πrh
Given that the radius (r) is 3 feet, we can substitute the values and rearrange the formula to solve for the height (h):
395.64 = 2 * 3.14 * 3 * h
395.64 = 18.84h
h = 395.64 / 18.84
h ≈ 21
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 21 feet.
Given:
Lateral Surface Area = 395.64 feet²
Radius of the circular bases = 3 feet
π = 3.14
We know that the lateral surface area of a cylinder is given by:
Lateral Surface Area = height x circumference of the base
The circumference of the base can be calculated as:
Circumference = 2πr
Circumference = 2 * 3.14 * 3
Circumference = 18.84 feet
We are given the lateral surface area as 395.64 feet². The lateral surface area can also be calculated using the formula:
Lateral Surface Area = 2πrh
Given that the radius (r) is 3 feet, we can substitute the values and rearrange the formula to solve for the height (h):
395.64 = 2 * 3.14 * 3 * h
395.64 = 18.84h
h = 395.64 / 18.84
h ≈ 21
Therefore, the height of the rectangle in the net diagram of the right circular cylinder is approximately 21 feet.