Question

A solid is hemispherical at the bottom and conical above it. The surface areas of the two parts are equal .The ratio of the volume of hemispherical part of the conical part is

• A. $2:\sqrt{3}$
• B. $1:1$
• C. $1:\sqrt{3}$
• D. $3:\sqrt{3}$

Answer 1

The correct option is A $2:\sqrt{3}$

S.A of cone = S.A of hemisphere
$\pi rl=2\pi r^2$
$\Rightarrow l=2r$
Now $h^2=t^2-r^2=3r^2\Rightarrow h=r\sqrt{3}$
Now $\frac{volumeofhemisphere}{volumeofcone}$
$\frac{\frac{2}{3}\pi r^3}{\frac{1}{3}\pi r^3\left(r\sqrt{3}\right)}=\frac{2}{\sqrt{3}}$