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):

$\text{Volume of cone:} \ \dfrac{1}{3} \times \pi \times r^{2} \times h$

[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.

    $\implies \text{Volume of cone:} \ \dfrac{1}{3} \times \pi \times (9)^{2} \times (10)$

∴ Let π be 3.14 ∴

    $\implies\text{Volume of cone:} \ \dfrac{1}{3} \times 3.14 \times (9)^{2} \times (10)$

Simplify the expression to determine the volume.

    $\implies\text{Volume of cone:} \ \dfrac{1}{3} \times 3.14 \times 81 \times 10$

    $\implies\text{Volume of cone:} \ 3.14 \times 27 \times 10$

    $\implies\text{Volume of cone:} \ 31.4 \times 27$

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