Question

If the radius of a sphere is halved, what happens to the volume of the sphere? Use your algebra skills to develop a formula for the volume of the reduced sphere, V', in terms of V.

Answer 1

to find the volume of a sphere is V=4/3 x π x r^2

Answer 2

\[V=\frac{ 4 }{ 3 } \times \pi r^3\]
\[V \prime=\frac{ 4 }{ 3 }\times \pi \times ( \frac{ r }{ 2 })^3=\frac{ 1 }{ 8 }\times \frac{ 4 }{ 3 } \pi r^3 =\frac{ 1 }{ 8 } V\]