Multiple choice

The volume of a cylinder is $\displaystyle 448\pi : cm^{3}$ and height is $7$ cm The lateral surface area of cylinder is

  1. $252$ $\displaystyle cm^{2}$
  2. $300$ $\displaystyle cm^{2}$
  3. $352$ $\displaystyle cm^{2}$
  4. $400$ $\displaystyle cm^{2}$
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C Correct answer
Explanation

Volume V = pi * r^2 * h = 448pi. With h=7, r^2 = 448/7 = 64, so r = 8. Lateral surface area = 2 * pi * r * h = 2 * pi * 8 * 7 = 112pi. 112 * 3.14159 = 351.85, which is 352.

AI explanation

Using the cylinder volume formula V = pi * r^2 * h, we substitute the given values to find the radius: 448 * pi = pi * r^2 * 7. Solving for r^2 gives 64, so the radius is 8 cm. The lateral surface area formula is * pi * r * h, which equals 2 * (22/7) * 8 * 7 = 352 square cm.

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