A rectangle, one of the sides of which is 5cm, revolves around the unknown side.

univerkov | May 30, 2021 | education

A rectangle, one of the sides of which is 5cm, revolves around the unknown side. Find the area of a rectangle if the lateral surface area of the cylinder obtained by rotation is 60π cm2.

The lateral surface area of the cylinder can be found using the following formula:

Sbp = 2πrh, where r is the radius of the base of the cylinder, and h is its height.

In this case, the base radius is equal to the length of the known side of the rectangle and is equal to 5 cm, and h is the unknown side of the rectangle. Let us express the height of the cylinder from the above formula:

h = Sbp / 2πr.

Now let’s find it:

h = 60π / (2π * 5) = 60π / 10π = 6 cm.

This means that the unknown side of the rectangle is also 6 cm.

The area of a rectangle can be found by multiplying the lengths of its sides. Let’s find the area of this rectangle:

S = 5 * 6 = 30 cm².

Answer: the area of the rectangle is 30 cm².

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