Question

The height of the frustum cone is $24$ ft. The area of the top and bottom circle of the cone is $6f{t}^2$ and $10f{t}^2$ respectively. Find its volume.

• A. $369f{t}^3$
• B. $367f{t}^3$
• C. $368f{t}^3$
• D. $362f{t}^3$

Answer 1

The correct option is C $368f{t}^3$

Volume of the frustum cone is $V=\frac{h}{3}[\pi R^2+\pi r^2+\sqrt{\left(\pi R^2\right)\left(\pi r^2\right))}]$
Area of the top cone $=10f{t}^2$
Area of the bottom cone $=90f{t}^2$
Height $=24$ ft
Volume = $\frac{24}{3}[90+10+\sqrt{10\times 90}]$
= $8[16+\sqrt{900}]$
= $8\left[46\right]$
= $368f{t}^3$