Q11
ArithmeticGeometry & Mensuration
The shape of the lower portion of a solid is hemisphere and the shape of upper portion of it is right circular cone. If the surface areas of two parts are equal, find the ratio of the radius and height of the cone
- a.$1 : \sqrt{3}$
- b.$\sqrt{3} : 1$
- c.$2 : \sqrt{3}$
- d.$\sqrt{3} : 2$
Answer: (A) $1 : \sqrt{3}$
Equating the curved surfaces, $2\pi r^2 = \pi r l$, so the slant height $l = 2r$. Then $h = \sqrt{l^2 - r^2} = \sqrt{3}r$, so $r : h = 1 : \sqrt{3}$. Option B reverses the ratio, and C and D come from using the wrong relation between $l$ and $h$.