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

Answer:

The diameter of the sphere is 6 centimeters

Step-by-step explanation:

we know that

The surface area of a sphere is

$SA=4\pi r^{2}$

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

Equate both formulas

$\frac{4}{3}\pi r^{3}=4\pi r^{2}$

Simplify

$\frac{1}{3}r^{3}=r^{2}$

$\frac{r^3}{r^2}=3$

$r=3\ cm$

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