Multiple choice

The sum of the radius of the base and the height of a closed solid cylinder is 12.5 cm. If the total surface area of the cylinder is 275 cm2, then its radius is (take ( \pi = \frac{22}{7} ))

  1. 7 cm

  2. 4 cm

  3. 3.5 cm

  4. 4.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let r + h = 12.5 cm. Total surface area = 2πr² + 2πrh = 2πr(r + h) = 2πr(12.5) = 275. Substituting π = 22/7: 2 × (22/7) × r × 12.5 = 275. Solving: r = 275 × 7 / (2 × 22 × 12.5) = 1925/550 = 3.5 cm. The formula 2πr(r+h) elegantly uses the given sum of radius and height.

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