Question

the volume of a right circular cone whose radius of the base is nine times its altitude is a ninth of the volume of a sphere. the ratio of the radii of the cone and sphere is

Answer 1

Dear Student,

Height of cone = h
Radius of cone, R = 9 * h
h = R / 9
Radius of sphere = r

Volume of cone = (1/9) * volume of sphere
$\frac{1}{3}$ * π * R² * h = $\frac{1}{9}$ * $\frac{4}{3}$ * π * r^{3
​​​​​}$\frac{1}{3}$ * π * R² * $\frac{R}{9}$ = $\frac{1}{9}$ * $\frac{4}{3}$ * π * r³
$\frac{R^3}{r^3}$ = 4
$\frac{R^{}}{r^{}}$ = 2^2/3

Regards,