Question

if the number of square centimetire on the surface of a sphear is equal to the number of cubic centimetres in its volume what is the diameter of the sphere​

Answer 1

The diameter of the sphere is 6 centimeters

Explanation:

we know that

The surface area of a sphere is

`SA=4\pi r^(2)`

The volume of the sphere is

`V=(4)/(3)\pi r^(3)`

Equate both formulas

`(4)/(3)\pi r^(3)=4\pi r^(2)`

Simplify

`(1)/(3)r^(3)=r^(2)`

`(r^3)/(r^2)=3`

`r=3\ cm`

Remember that the diameter is two times the radius

so

`D=2r=2(3)=6\ cm`

therefore

The diameter of the sphere is 6 centimeters