Question

If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere

Answer 1

The radius of the sphere will be:

• 
  `r=3.1` units

Explanation:

Given that a sphere has the same volume as a cube with edge length 5.

`V_c=V_s`

`\:a^3=(4)/(3)\pi r^3`

`\:r^3=(3\:a^3)/(4\pi )`

`\:\:r=\sqrt[3]{(3\:a^3)/(4\pi \:)\:\:}`

substitute a = 5

`r=\sqrt[3]{(3\:\left(5\right)^3)/(4\pi \:\:\:)\:\:}`

`r=3.1` units

Therefore, the radius of the sphere will be:

• 
  `r=3.1` units