Question

Keep the radius the same but use a different height is the volume of the sphere 2/3 the volume of the cylinder now explain your answer

Answer 1

From geometry, we know that:

• the volume of a sphere of radius r is:

`V_S=(4)/(3)\cdot\pi\cdot r^3,`

• the volume of a cylinder of radius r and heigth h is:

`V_C=h\cdot\pi\cdot r^2.`

If the volume of the sphere (Vs) is 2/3 the volume of the cylinder (Vc), we have:

`\begin{gathered} V_S=(2)/(3)\cdot V_C, \\ (4)/(3)\cdot\pi\cdot r^3=(2)/(3)\cdot h\cdot\pi\cdot r^2. \end{gathered}`

Solving for h, we find that:

`h=2r.`

We have found that the height of the cylinder is two times its radius.

Answer

• We have a sphere and cylinder with the same radius.

,

• We know that the volume of the sphere is

`V_S=(2)/(3)\cdot V_C.`

• By replacing the formulas of each volume, we find that the heigh of the cylinder is:

`h=2r.`