Multiple choice

If the lateral surface of a cylinder is 94.2 cm$^2$ and its height is 5 cm, then find (i) radius of its base. (ii) its volume(Use $\pi=3.14$).

  1. $r=3cm,volume=141.3cm^3$
  2. $r=2cm,volume=151.3cm^3$
  3. $r=5cm,volume=171cm^3$
  4. $r=3cm,volume=162cm^3$
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A Correct answer
Explanation

Lateral surface area = 2*pi*r*h = 94.2. With h=5 and pi=3.14, 2*3.14*r*5 = 94.2, so 31.4*r = 94.2, r=3. Volume = pi*r^2*h = 3.14*9*5 = 141.3.

AI explanation

Using the lateral surface area formula for a cylinder, LSA = 2 pi r h, we substitute the known values to get 94.2 = 2 times 3.14 times r times 5. This simplifies to 94.2 = 31.4 r, yielding a base radius r of 3 cm. We then apply the cylinder volume formula, V = pi r squared h, to get V = 3.14 times (3 squared) times 5, which equals 3.14 times 9 times 5, resulting in a volume of 141.3 cubic cm.

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