Find the volume of the first cylinder if its height is two times less, and the radius of the base is three times greater

| August 10, 2021 | education

Find the volume of the first cylinder if its height is two times less, and the radius of the base is three times greater than that of the second cylinder, and the volume of the second cylinder is 16.

h1 = h2 / 2.

r1 = 3 * r2.

V2 = 16.

V1 -?

The volume of the cylinder V is determined by the formula: V = S * h, where S is the area of the base of the cylinder, h is the height of the cylinder.

The area S of the base of the cylinder has the shape of a circle, therefore S = P * r ^ 2, where P is the number pi, r is the radius of the base of the cylinder.

V = P * r ^ 2 * h.

Let’s express the volume of the first and second cylinders.

V2 = P * r2 ^ 2 * h2.

V1 = P * r1 ^ 2 * h1 = P * (3 * r2) ^ 2 * h2 / 2 = P * 9 * r2 ^ 2 * h2 / 2 = 9 * V2 / 2 = 9 * 16/2 = 72.

Answer: the volume of the first cylinder is V1 = 72.



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