Question

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Which statement about the radius of the sphere is true

Answer 1

Radius of sphere is 3 units.

Explanation:

Volume of sphere is given by
`4/3 \pi r^3`

surface area of sphere is given by
`4 \pi r^2`

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere and surface area of sphere

assuming r as the radius.

thus,

`4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3`

Thus, radius of sphere is 3 units.