Multiple choice

Find the height of a cylinder whose radius is $10\;cm$ and the total surface area is $2420\;cm^2$.

  1. $28.5\;cm$
  2. $285\;cm$
  3. $56.5\;cm$

  4. None of these
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A Correct answer
Explanation

Total surface area of a cylinder is 2*pi*r*(r + h) = 2420. Given r = 10, 2*pi*10*(10 + h) = 2420. Using pi = 22/7, 440/7 * (10 + h) = 2420. 10 + h = 2420 * 7 / 440 = 38.5. Thus, h = 28.5 cm.

AI explanation

Using the total surface area formula for a cylinder, 2 * pi * r * (r + h) = 2420. Substituting the radius r = 10 gives 2 * (22/7) * 10 * (10 + h) = 2420. Solving for h involves simplifying to (10 + h) = 2420 * 7 / 440, which equals 38.5. Subtracting 10 gives a height of 28.5 cm.

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