The circumference of the base of a solid right circular cylinder is 132 cm and…

CONCEPT

For a right circular cylinder, the base circumference and volume are C = 2πr and V = πr2h.

First find the radius from the circumference, then use that radius with the height in the volume formula. All dimensions must use the same unit.

APPLICATION

1. Let r be the radius in centimetres. From C = 2πr, write 132 = 2 × (22/7) × r.

2. Solve for the radius: r = (132 × 7)/44 = 21 cm.

3. Use the cylinder-volume formula: V = πr2h.

4. Substitute the known values: V = (22/7) × 212 × 60.

5. Simplify in order: V = 22 × 63 × 60 = 1,386 × 60 = 83,160 cm3.

CROSS-CHECK

1. The recovered radius gives circumference 2 × (22/7) × 21 = 132 cm, matching the given value.

2. The base area is (22/7) × 212 = 1,386 cm2; multiplying by height 60 cm gives 83,160 cm3.

Therefore, the cylinder volume is 83,160 cm3.