Multiple choice

The volume of a cylinder is $\displaystyle 400{ m }^{ 3 }$ and its radius $7 m$. Find its total surface area of a cylinder.

  1. $\displaystyle 140.5{ m }^{ 2 }$
  2. $\displaystyle 422.02{ m }^{ 2 }$
  3. $\displaystyle 150.2{ m }^{ 2 }$
  4. $\displaystyle 142.8{ m }^{ 3 }$
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B Correct answer
Explanation

Volume V = pi * r^2 * h = 400. With r=7, 400 = pi * 49 * h, so h = 400 / (49 * pi) approx 2.598. Total surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 2.598) approx 422.02.

AI explanation

Using the cylinder volume formula, V = pi * r^2 * h, we find the height: 400 = (22/7) * 7^2 * h, which simplifies to h = 400/154 or about 2.5974 meters. Then, apply the total surface area formula, 2 * pi * r * (h + r), to get 2 * (22/7) * 7 * (2.5974 + 7). This calculates to approximately 422.02 square meters.

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