Find the surface area of a cylinder with a height of 12 meters and a diameter of 14 meters. Use 3.14 for π and round to the nearest tenth.
The formula for the surface area of a cylinder is:
Surface Area = 2πr(r + h)
Given that the diameter is 14 meters, the radius is half of that, which is 7 meters.
Also, the height of the cylinder is 12 meters.
Substituting these values into the formula:
Surface Area = 2(3.14)(7)(7 + 12)
Surface Area = 2(3.14)(7)(19)
Surface Area = 2(3.14)(133)
Surface Area = 2(417.62)
Surface Area = 835.24
Rounding to the nearest tenth:
Surface Area ≈ 835.2 square meters
Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi.
To find the surface area of the cone peak, we need to calculate the lateral surface area of the cone.
The formula for the lateral surface area of a cone is:
Lateral Surface Area = πrℓ
Given that the diameter is 14 inches, the radius is half of that, which is 7 inches.
Also, the slant height of the cone is given as 20 inches.
Substituting these values into the formula:
Lateral Surface Area = 3.14 * 7 * 20
Lateral Surface Area = 439.6
Rounding to the nearest hundredth:
Lateral Surface Area ≈ 439.6 square inches
A water bottle has a height of 16 inches and a radius of 4 inches. What is the volume, in cubic inches, of the water bottle? Use 3.14 for pi.
The formula to calculate the volume of a cylinder is:
Volume = πr^2h
Given that the radius is 4 inches and the height is 16 inches, we can substitute these values into the formula:
Volume = 3.14 * 4^2 * 16
Volume = 3.14 * 16 * 16
Volume = 3.14 * 256
Volume = 804.64
The volume of the water bottle is approximately 804.64 cubic inches.
are you sure?
Apologies for the mistake. Let me recalculate the volume correctly.
The formula for calculating the volume of a cylinder is:
Volume = πr^2h
Given that the radius is 4 inches and the height is 16 inches, we can substitute these values into the formula:
Volume = 3.14 * 4^2 * 16
Volume = 3.14 * 16 * 16
Volume = 3.14 * 256
Volume ≈ 804.48
The correct volume of the water bottle is approximately 804.48 cubic inches.
What is the volume of a cylinder with a base radius of 8 in. and a height of 40 in.?
To find the volume of a cylinder, we can use the formula:
Volume = πr^2h
Given that the base radius is 8 inches and the height is 40 inches, we can substitute these values into the formula:
Volume = 3.14 * 8^2 * 40
Volume = 3.14 * 64 * 40
Volume = 3.14 * 2560
Volume ≈ 8041.6
The volume of the cylinder is approximately 8041.6 cubic inches.