Radius and diameter of a sphere are, respectively, equal to the base radius and height of a cone. Find the ratio of their volumes.

Question

Radius and diameter of a sphere are, respectively, equal to the base radius and height of a cone. Find the ratio of their volumes. (A) 1: 2 (B) 2: 3 (C) 4: 3 (D) 2: 1

Tardigrade Admin · Accepted Answer

Let the radius of the sphere be r mathrm~cm. ∴ text Diameter =2 mathrmrcm Base radius of the cone =r mathrm~cm Height =2 r mathrm~cm (given) ∴ text Required ratio =((4/3) π r3/(1)3 π r2(2 r)) (∴ h=2 r) =(4/2)=2: 1

Q. Radius and diameter of a sphere are, respectively, equal to the base radius and height of a cone. Find the ratio of their volumes.

$1 : 2$

$2 : 3$

$4 : 3$

$2 : 1$

Let the radius of the sphere be $r cm$ .
$∴ Diameter = 2 rcm$
Base radius of the cone $= r cm$
Height $= 2 r cm$ (given)
$∴ Required ratio = \frac{\frac{4}{3} π r ^{3}}{\frac{1}{3} π r ^{2} ( 2 r )} (∴ h = 2 r)$
$= \frac{4}{2} = 2 : 1$