# A rectangle with sides of 3cm and 5cm rotates around the larger side. Find the volume of the body of revolution.

July 25, 2021 | education

| The result of the rotation of a rectangle around one of its sides is a cylinder – a known body of revolution (there is also a cone and a ball, if that).

The volume of the cylinder is found by the formula: V = Sbn • h. At the base of the cylinder lies a circle, its area: S = nR ^ 2.

Since the rotation is about a side 5 cm long, h = 5 cm is the height of the cylinder. But 3 cm is the radius obtained at the base of the circle R = 3 cm.

Total:

V = Sbase • h = S = nR ^ 2 • h = n • 3 ^ 2 • 5 = 45n (cm3).

A more accurate value can be found by replacing n = 3.14:

V = 45 * 3.14 = 141.3 (cm3).

Answer: V = 45p cm3 = 141.3 cm3.

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