Question

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

Answer 1

Answer:

hope it helps you mate.

Answer 2

r:h = $1:\sqrt{3}$

Step-by-step explanation:

Radius of hemisphere and cone = r

slant height of the cone = l

curved surface area of the hemisphere = $2\pi r^2$

curved surface area of the cone = $\pi rl$

according to the question

curved surface area of the hemisphere = curved surface area of the cone

$2\pi r^2$ = $\pi rl$

2r = l

putting the value of l (slant height ) = $\sqrt{h^2 + r^2}$

2r =  $\sqrt{h^2 + r^2}$

on squaring both side we get,

(2r)² = $(\sqrt{h^2 + r^2})^2$

4r² = h²+r²

4r²-r² = h²

3r² =h²

$\frac{r^2}{h^2}$ = $\frac{1}{3}$

$(\frac{r}{h})^2$ = $\frac{1}{3}$

$\frac{r}{h}$ = $\sqrt{\frac{1}{3} }$

$\frac{r}{h}$ = $\frac{1}{\sqrt{3} }$

hence,

the ratio of the radius and the height of conical part

r:h = $1:\sqrt{3}$

#Learn more:

A solid is hemispherical at the bottom and conical above . if the surface areas of the two parts are equal , then the ratio of its radius and the height of its conical part is..

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