Question

a sphere has a radius of 3 and a hemisphere has a radius of 6. compare ratio of vulume of the sphere to the volume of the hemisphere

Answer 1

\[V=\frac{ 4 \pi r³ }{ 3 }\]Volume of the sphere:\[V=\frac{ 4 \pi *3³ }{ 3 } = \frac{ 4 \pi *27 }{ 3 } = 36 \pi\]Volume of the hemisphere (remember that a hemisphere withs a half from a planet):\[V=\frac{ 4 \pi *6³ }{ 3 } * \frac{1}{2}= \frac{ 4 \pi *216 }{ 3 } * \frac{1}{2}= 144 \pi\]

Ratio = \[\frac{ 36\pi }{ 144 \pi } = \frac{1}{4}\]