Question

Find the volume of a cone with base area 36π ft2 and a height equal to twice the radius. Give your answers both in terms of π and rounded to the nearest tenth.

The volume in terms of π is _____ft3.
The volume rounded to the nearest tenth is _____ft3.

Answer 1

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Explanation:

The formula of the volume of a cone is V =
`(1)/(3)` π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

∵ The area of the base of the cone is 36π ft²

- Equate the formula of the area of the circle by 36π to find r

∵ πr² = 36π

- Divide both sides by π

∴ r² = 36

- Take √ to both sides

∴ r = 6 ft

∵ The height of the cone is equal to twice the radius

∵ The radius of the cone is 6 ft

- Multiply 6 by 2 to find the height

∴ h = 2(6) = 12 ft

∴ The height of the cone is 12 ft

Substitute the values of h and r in the formula of the volume of the cone to find it

∵ V =
`(1)/(3)` π(6)²(12)

∴ V = 144 π ft³

∴ V = 452.3893421 ft³

- Round it to the nearest tenth

∴ V = 452.4 ft³