Question

The radius of a sphere is $p$ units and the radius of a hemisphere is $2p$ units. What is the ratio of the volume of the sphere to the volume of the hemisphere

Answer 1

Answer: $\frac{V_{s}}{V_{h}} = \frac{1}{4}$

Step-by-step explanation: A Hemisphere is a half of a sphere.

Volume of sphere is calculated as:

$V_{s}=\frac{4}{3}.\pi.r^{3}$

then, volume of a hemisphere is:

$V_{h}=\frac{1}{2} \frac{4}{3} .\pi.r^{3}$

Sphere with radius p has volume:

$V_{s}=\frac{4}{3}.\pi.p^{3}$

Hemisphere with radius 2p has volume:

$V_{h}=\frac{1}{2} \frac{4}{3} .\pi.(2p)^{3}$

$V_{h}=\frac{1}{2} \frac{4}{3} .\pi.8p^{3}$

Ratio of the volumes of sphere to hemisphere will be:

$\frac{V_{s}}{V_{h}}=\frac{4/3.\pi.r^{3}}{4/6.\pi.8.p^{3}}$

$\frac{V_{s}}{V_{h}} =(\frac{4}{3}.\pi.p^{3})(\frac{6}{4.\pi.8p^{3}})$

$\frac{V_{s}}{V_{h}}=\frac{1}{4}$

Ratio of the volume of the sphere to the volume of the hemisphere is $\frac{1}{4}$, which means volume of the hemisphere is 4x the volume of the sphere.