Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3

Answer 1

Answer:

12 cm³

Step-by-step explanation:

Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.

The volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius.

The volume of a cylinder is denoted by: $V=\pi r^2h$, where r is the radius and h is the height. Plug in 2r for h and 18 for V:

$V=\pi r^2h$

$18=\pi r^2*2r=2\pi r^3$

$\pi r^3=18/2=9$

Now plug in 9 for πr³ in the volume formula for the sphere:

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

$V=\frac{4}{3} *9=12$

The volume of the sphere is 12 cm³.