The volume of the cylinder 36. Find the volume if the height is reduced by six times and the radius

The volume of the cylinder 36. Find the volume if the height is reduced by six times and the radius is increased by three times?

The volume of the cylinder is equal to the area of the circle at the base multiplied by the height h1.

1) v1 = s1 (circle) * h1 = (pi * r1 ^ 2 * h1) = 36. (1)

2) Reducing the height of h1 by 6 times, we get h2 = (1/6) * h1.

Let’s increase the radius of the circle by 3 times, we get r2 = 3 * r1.

3) Calculate the changed volume of the cylinder:

v2 = s2 (circle) * n2 = pi * r2 ^ 2 * n2 = pi * (3 * r1) ^ 2 * n1 / 6 =

(pi * r1 ^ 2 * h1) * (3 ^ 2/6).

The expression in the first parenthesis according to formula (1) is v1 = 36.

Let’s insert the value v1 into the formula v2:

v2 = v1 * (9/6) = 1.5 * v1 = 1.5 * 36 = 54.

Answer: the volume is 54.