A solid cylinder has a total surface area of 352 cm2. Its curved surface area is one-eighth of the total surface area. The radius (in cm) of the cylinder is:
[Use π = 22/7]
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 7.
Total surface area = 352 cm²
Curved surface area = 1/8 of 352 = 44 cm²
Curved surface area of a cylinder = 2πrh = 2 × 22/7 × r × h = 44
⇒ (44/7) × r × h = 44 → r × h = 7 → (1)
Total surface area = 2πr² + 2πrh
→ 2 × 22/7 × r × (r + h) = 352 → (44/7) × r × (r + h) = 352 → (2)
From (1): h = 7/r Put into (2):
(44/7) × r × (r + 7/r) = 352 → (44/7) × (r² + 7) = 352
→ 44 × (r² + 7) = 2464 → r² + 7 = 56 → r² = 49 → r = 7