A solid cylinder has total surface area 462 sq cm. If its curved surface area…
2016
A solid cylinder has total surface area 462 sq cm. If its curved surface area is one-third of its total surface area, then the volume of the cylinder will be
Answer: B. 539 cubic cm — For any solid (closed) cylinder of radius r and height h: Total Surface Area (TSA) = Curved Surface Area (CSA) + area of the two circular bases, i.e. TSA =…
- A.
639 cubic cm
- B.
539 cubic cm
- C.
439 cubic cm
- D.
600 cubic cm
Show answer & explanation
Correct answer: B
For any solid (closed) cylinder of radius r and height h: Total Surface Area (TSA) = Curved Surface Area (CSA) + area of the two circular bases, i.e. TSA = 2πrh + 2πr2, and Volume = πr2h. Once the CSA is known as a fraction of the TSA, the base-area term 2πr2 is fixed, which pins down r, then h, then the volume.
Curved Surface Area = one-third of Total Surface Area = (1/3) × 462 sq cm = 154 sq cm.
Since TSA = CSA + 2πr2, the base-area term 2πr2 = 462 − 154 = 308 sq cm.
Taking π ≈ 22/7: 2 × (22/7) × r2 = 308, so r2 = 49, giving r = 7 cm.
From CSA = 2πrh: 154 = 2 × (22/7) × 7 × h = 44h, so h = 3.5 cm.
Volume = πr2h = (22/7) × 49 × 3.5 = 539 cubic cm.
Check: CSA + 2πr2 = 154 + 308 = 462, which equals the given total surface area, and 154 is exactly one-third of 462 — confirming the radius and height obtained are consistent.
So, using π = 22/7 — the convention the clean radius value of 7 cm confirms is intended here — the volume works out to exactly 539 cubic cm.