Multiple choice

The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is (1232 cm^2), What is the height?

  1. 14 cm

  2. 28 cm

  3. 7 cm

  4. 56 cm

  5. 24 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cylinder, curved surface area (CSA) = 2πrh and total surface area (TSA) = 2πr(r + h). Given CSA:TSA = 4:5, so 2πrh / 2πr(r+h) = 4/5. Simplifying: h/(r+h) = 4/5, so 5h = 4r + 4h, giving h = 4r. With CSA = 1232 = 2πrh = 2πr(4r) = 8πr². Solving: r² = 1232/(8π) ≈ 49, so r = 7. Height h = 4r = 28 cm. Option B is correct.

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