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:
`(V_(s))/(V_(h)) = (1)/(4)`

Explanation: A Hemisphere is a half of a sphere.

Volume of sphere is calculated as:

`V_(s)=(4)/(3).\pi.r^(3)`

then, volume of a hemisphere is:

`V_(h)=(1)/(2) (4)/(3) .\pi.r^(3)`

Sphere with radius p has volume:

`V_(s)=(4)/(3).\pi.p^(3)`

Hemisphere with radius 2p has volume:

`V_(h)=(1)/(2) (4)/(3) .\pi.(2p)^(3)`

`V_(h)=(1)/(2) (4)/(3) .\pi.8p^(3)`

Ratio of the volumes of sphere to hemisphere will be:

`(V_(s))/(V_(h))=(4/3.\pi.r^(3))/(4/6.\pi.8.p^(3))`

`(V_(s))/(V_(h)) =((4)/(3).\pi.p^(3))((6)/(4.\pi.8p^(3)))`

`(V_(s))/(V_(h))=(1)/(4)`

Ratio of the volume of the sphere to the volume of the hemisphere is
`(1)/(4)`, which means volume of the hemisphere is 4x the volume of the sphere.