The circumference of the base of a right circular cylinder is 528 cm and its…
2019
The circumference of the base of a right circular cylinder is 528 cm and its height is 2 m. What is the volume of the cylinder? (Take pi = 22/7)
- A.
2.2176 m³
- B.
3.3264 m³
- C.
4.4352 m³
- D.
6.6528 m³
Show answer & explanation
Correct answer: C
Concept: For a right circular cylinder, the circumference of the circular base relates to the radius by C = 2πr, and the volume is V = πr2h, where r is the base radius and h is the height.
Application:
From the circumference C = 2πr, find the radius: r = C ÷ (2π) = 528 ÷ (2 × 22/7) = (528 × 7) ÷ 44 = 84 cm.
Convert the height to the same unit as the radius: h = 2 m = 200 cm.
Apply the volume formula: V = πr2h = (22/7) × 842 × 200.
Compute 842 = 7056, then (22/7) × 7056 = 22 × 1008 = 22176.
Multiply by the height: 22176 × 200 = 44,35,200 cm3.
Convert to cubic metres (1 m3 = 10,00,000 cm3): 44,35,200 ÷ 10,00,000 = 4.4352 m3.
Cross-check: Converting to metres first gives the same result — r = 0.84 m, h = 2 m, so V = πr2h = (22/7) × 0.842 × 2 = (22/7) × 0.7056 × 2 = 22 × 0.1008 × 2 = 4.4352 m3, confirming the volume.