Question

A hemisphere and a cone have equal bases if their heights are also equal then the ratio of the curved surface area will be

Answer 1

Let the radius of hemisphere and cone be R, 
Height of hemisphere H = R.
So the height of the cone = height of the hemisphere = R
Slant height of the cone 
\begin{aligned}
= \sqrt{R^2+R^2} \\
= \sqrt{2}R \\
\frac{\text{Hemisphere Curved surface area}}{\text{Cone Curved surface area}} = \\
\frac{2\pi R^2}{\pi *R*\sqrt{2}R} \\
= \sqrt{2}:1
\end{aligned}

Answer 2

Hi dear here is your answer.