Multiple choice

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Directions: Study the following information carefully and answer the given question. There is a solid cylinder of radius R cm and height h cm. The height of cylinder is 21 cm more than the radius of cylinder. The ratio of the total area of the solid cylinder to the curved surface area of cylinder is 3 : 2. This solid cylinder is cut along vertical axis in N equal pieces. Later it was found that the total surface area has increased by 5292 sq.cm.

Find the radius (R) of the cylinder.

  1. 35 cm

  2. 30 cm

  3. 42 cm

  4. 21 cm

  5. 28 cm
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D Correct answer
Explanation

Let R be radius, h = R + 21. Total surface area (TSA) = 2*pi*R*(R+h) = 2*pi*R*(2R+21). Curved surface area (CSA) = 2*pi*R*h = 2*pi*R*(R+21). Ratio TSA/CSA = (2R+21)/(R+21) = 3/2. Solving gives 4R + 42 = 3R + 63, so R = 21.

AI explanation

The ratio of the total surface area to the curved surface area is 3 : 2, so (2*pi*R*h + 2*pi*R^2) / (2*pi*R*h) equals 3/2. Simplifying this gives 1 + (R/h) = 1.5, which means R/h is 1/2, or h = 2R. Since the height is 21 cm more than the radius, substituting h gives 2R = R + 21. Solving this yields R = 21 cm.

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