Question

The formula for the volume V of a cylinder with radius r and height h is as follows.

V = π r^2 h

Suppose the radius of the cylinder is 5 times the height. Rewrite V in terms of h only.

Answer 1

The volume V of a cylinder, when the radius r is 5 times the height h, can be rewritten in terms of h only as V = 25πh³.

Step-by-step explanation:

To rewrite the formula for the volume V of a cylinder in terms of the height h only, when the radius r is 5 times the height, we first represent the radius in terms of h:

r = 5h

The original formula for the volume of a cylinder is:

V = πr²h

Substituting r with 5h, we have:

V = π(5h)²h

V = π(25h²)h

V = 25πh³

Therefore, the volume of the cylinder in terms of h only is V = 25πh³.