Question

The volume of the cone is $\frac{8}{3}$ cu ft and its base area is $7\frac{1}{2}$ sq ft.

The height of the right circular cone is ft.

• A. $\frac{16}{15}$
• B. $\frac{15}{16}$
• C. $\frac{16}{15}$
• D. $\frac{4}{15}$

Answer 1

The correct option is A $\frac{16}{15}$

Given:
Base area = $7\frac{1}{2}$ sq ft = $\frac{15}{2}$ sq ft
Volume of the cone = $\frac{8}{3}$ cu ft

We know that,
Volume of a cone =$\frac{1}{3}$ × Base area × Height
$\Rightarrow$ $\frac{8}{3}$ = $\frac{1}{3}$ × $\frac{15}{2}$ × h
$\Rightarrow$ $\frac{8}{3}$ = $\frac{5}{2}$ × h
$\Rightarrow$$\frac{8}{3}$ ÷ $\frac{5}{2}$ = $\frac{5}{2}$ ÷ $\frac{5}{2}$ x h
$\Rightarrow$h = $\frac{8}{3}$ x $\frac{2}{5}$
$\Rightarrow$h = $\frac{16}{15}$

Hence, the height of the cone is $\frac{16}{15}$ ft.