How many times will the area of the lateral surface of the cylinder increase if its height

univerkov | August 13, 2021 | education

How many times will the area of the lateral surface of the cylinder increase if its height is reduced by 3 times, and the radius is increased by 6 times.

Let the radius of the first cylinder be OA = R1 cm, and the height AB = h1 cm.

Then the area of the lateral surface of the original cylinder is equal to:

S1 side = 2 * π * R1 * h1.

The radius of the base of the second cylinder is equal to: ОА = 6 * R1 cm, and its height AB = h1 / 3 cm.

The lateral surface area of the second cylinder is:

S2 side = 2 * π * 6 * R1 * h1 / 3 = 4 * π * R1 * h1.

Then S2 side / S1 side = 4 * π * R1 * h1 / 2 * π * R1 * h1 = 2.

Answer: The lateral surface area will double.

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