Question

A cone has a height of 10 yards and a radius of 9 yards. What is its volume?

Use 3.14 and round your answer to the nearest hundredth.
cubic yards

Answer 1

Part I: Recalling the "Volume of cone" formula

Given:

• Height of cone = 10 yards

• Radius of cone = 9 yards

Formula (Volume of cone):

`\text{Volume of cone:} \ (1)/(3) * \pi * r^(2) * h`

[Where r and h are the radius and the height respectively.]

Part II: Determining the volume of the cone

Substitute their values into the formula to determine the volume of the cone.

`\implies \text{Volume of cone:} \ (1)/(3) * \pi * (9)^(2) * (10)`

∴ Let π be 3.14 ∴

`\implies\text{Volume of cone:} \ (1)/(3) * 3.14 * (9)^(2) * (10)`

Simplify the expression to determine the volume.

`\implies\text{Volume of cone:} \ (1)/(3) * 3.14 * 81 * 10`

`\implies\text{Volume of cone:} \ 3.14 * 27 * 10`

`\implies\text{Volume of cone:} \ 31.4 * 27`

`\implies\text{Volume of cone} = 847.8 \ \text{yd}^(3) = \boxed{847.80 \ \text{yd}^(3)} \ \ \ \ \ \ \ \ (\text{Nearest hundredth)}`