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Question 101
A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be
Solution
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 = $$\sqrt{R^2+R^2}$$
$$\frac{\text{Hemisphere Curved surface area}}{\text{Cone Curved surface area}}=\frac{2\pi R^2}{\pi R \sqrt{2}R}$$
√2 : 1
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