Multiple choice

The height and the radius of the base of a closed cylinder are in the ratio 3: 1. If its volume is 1029 $\displaystyle \pi:cm^{3};$ then its outer surface area is 526 $cm^2$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = pi * r^2 * h. Given h = 3r, Volume = pi * r^2 * (3r) = 3 * pi * r^3. 3 * pi * r^3 = 1029 * pi, so r^3 = 343, r = 7. Then h = 21. Surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 21) = 2 * pi * 7 * 28 = 392 * pi. 392 * pi is approx 1231.5, not 526.

AI explanation

Let the radius be x and the height be 3x. Using the cylinder volume formula, pi times x squared times 3x equals 1029 times pi, so x cubed equals 343, meaning the radius x is 7 cm and the height is 21 cm. The outer surface area formula for a closed cylinder is 2 times pi times r times (r plus h), which becomes 2 times pi times 7 times 28. This calculates to 392 times pi, which is approximately 1232 square cm, not 526 square cm, so the statement is false.

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