A hemisphere and a cone have equal bases. If | vedclass

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(B) Let the radius of the base of the hemisphere be $r$ units. Since the bases are equal,the radius of the cone is also $r$ units.Given that the heigh

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$2: \sqrt{2}$

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(B) Let the radius of the base of the hemisphere be $r$ units. Since the bases are equal,the radius of the cone is also $r$ units.Given that the heights are equal,the height of the cone $h = r$ (as the height of a hemisphere is equal to its radius).The slant height $l$ of the cone is given by $l = \sqrt{r^2 + h^2} = \sqrt{r^2 + r^2} = \sqrt{2r^2} = r\sqrt{2}$.The curved surface area of the hemisphere is $2\pi r^2$.The curved surface area of the cone is $\pi rl = \pi r(r\sqrt{2}) = \pi r^2\sqrt{2}$.The ratio of the curved surface area of the hemisphere to the curved surface area of the cone is $2\pi r^2 : \pi r^2\sqrt{2} = 2 : \sqrt{2}$.

$A$ hemisphere and a cone have equal bases. If their heights are also equal,the ratio of their curved surfaces will be

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