Respuesta :
Answer: [tex]\frac{V_{s}}{V_{h}} = \frac{1}{4}[/tex]
Step-by-step explanation: A Hemisphere is a half of a sphere.
Volume of sphere is calculated as:
[tex]V_{s}=\frac{4}{3}.\pi.r^{3}[/tex]
then, volume of a hemisphere is:
[tex]V_{h}=\frac{1}{2} \frac{4}{3} .\pi.r^{3}[/tex]
Sphere with radius p has volume:
[tex]V_{s}=\frac{4}{3}.\pi.p^{3}[/tex]
Hemisphere with radius 2p has volume:
[tex]V_{h}=\frac{1}{2} \frac{4}{3} .\pi.(2p)^{3}[/tex]
[tex]V_{h}=\frac{1}{2} \frac{4}{3} .\pi.8p^{3}[/tex]
Ratio of the volumes of sphere to hemisphere will be:
[tex]\frac{V_{s}}{V_{h}}=\frac{4/3.\pi.r^{3}}{4/6.\pi.8.p^{3}}[/tex]
[tex]\frac{V_{s}}{V_{h}} =(\frac{4}{3}.\pi.p^{3})(\frac{6}{4.\pi.8p^{3}})[/tex]
[tex]\frac{V_{s}}{V_{h}}=\frac{1}{4}[/tex]
Ratio of the volume of the sphere to the volume of the hemisphere is [tex]\frac{1}{4}[/tex], which means volume of the hemisphere is 4x the volume of the sphere.
