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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