Question

If height of a cone is $h$, its slant height is $l$, then radius of it's base will be:

• A. $\sqrt{l+h}$
• B. $\sqrt{l-h}$
• C. $\sqrt{h^2-l^2}$
• D. $\sqrt{l^2-h^2}$

Answer 1

The correct option is D $\sqrt{l^2-h^2}$

Assume radius $AB=r$.

Applying Pythagoras theorem in right angle triangle $ABC$,

$\Rightarrow l^2=h^2+r^2$

$\Rightarrow r^2=l^2-h^2$

$\Rightarrow r=\sqrt{l^2-h^2}$.

Hence, option $D$ is correct.