Question

The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?

Answer 1

We have that the volume of sphere is

`\begin{gathered} V_s=(4)/(3)\pi\cdot r^3 \\ \end{gathered}`

and the volume of a cube is

`V_c=s^3`

so if s=r=3. The volume of the sphere is greater.

If they have the same volume, we get that

`\begin{gathered} (4)/(3)\pi\cdot r^3=125\rightarrow \\ r^3=(3)/(4\cdot\pi)\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}`

when s=r=2 we have that

`\begin{gathered} V_s=(4)/(3)\pi\cdot8=(32)/(3)\pi \\ V_c=8 \end{gathered}`

so the volume of the sphere is greater