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  • A solid is in the shape of a cone mounted on a hemisphere of same base radius If the curved surface areas of the hemispherical part and the conical part are equal then find the ratio of the radius and the height of the conical part

A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.

 

 

 

 
 
 
 
 

Answers (1)

$ Radius of cone = radius of hemisphere = r $ \\ $ Curved surface area of hemisphere = curved surface area of cone $ \\\ 2 \pi r^2 = \pi r l \\ l = 2r \\ \sqrt{h^{2}+r^{2}}=2 r \\ h^2 + r^2 = 4r^2 \\ h^2 = 3r^2 \\ h= \sqrt{3} r \\ \frac{r}{h}= \frac{1}{\sqrt{3}}

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Safeer PP

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