Multiple choice

The lateral surface area of cylinder is $176{cm}^{2}$ and base area 38.5${cm}^{2}$. The volume is ..............

  1. $830 {cm}^{3}$
  2. $380{cm}^{3}$
  3. $308{cm}^{3}$
  4. $803{cm}^{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lateral surface area = 2 * pi * r * h = 176. Base area = pi * r^2 = 38.5. From base area, r^2 = 38.5 / (22/7) = 12.25, so r = 3.5. Then 2 * (22/7) * 3.5 * h = 176, so 22 * h = 176, h = 8. Volume = pi * r^2 * h = 38.5 * 8 = 308.

AI explanation

Using the base area formula, pi * r^2 = 38.5, and taking pi as 22/7, we find the radius r by solving r^2 = (38.5 * 7) / 22, which gives r = 3.5 cm. The lateral surface area formula is 2 * pi * r * h, so we solve 2 * (22/7) * 3.5 * h = 176 to get a height of 8 cm. Finally, calculate the cylinder volume using pi * r^2 * h, which gives 38.5 * 8 to equal 308 cubic cm.

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