Question

What is the volume of a cone of height h and radius $\frac{h}{2}$.

• A. $\frac{h^3\pi }{6}{\text{unit}}^3$
• B. $\frac{h^2\pi }{6}{\text{unit}}^3$
• C. $\frac{h^3\pi }{6}\text{unit}$
• D. $\frac{h^3\pi }{3}{\text{unit}}^3$

Answer 1

The correct option is A $\frac{h^3\pi }{6}{\text{unit}}^3$

Let's draw a cone of the given dimensions.
Given,
The radius of a cone $=r=\frac{h}{2}$ unit
The depth of a cone $=h=h$ unit

As we know,
The volume of a cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi \times {\frac{h}{2}}^2\times h$

$=\frac{\pi }{6}\times h^2\times h$

$=\frac{h^3\pi }{6}{\text{unit}}^3$