Multiple choice

Consider two cylinders($C_1$ and $C_2$), in which $C_1$'s height is double that of the height of other cylinder $C_2$ and their radius is half of the radius of $C_2$. Then find the volumes of these two cylinders and compare them.

  1. Volume of $C_1 > $ Volume of $C_2$
  2. Volume of $C_1=2 \times$ Volume of $C_2$
  3. Volume of $C_1= $ Volume of $C_2$
  4. Volume of $C_1=\dfrac{1}{2}\times $ Volume of $C_2$
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D Correct answer
Explanation

V1 = pi * (r/2)^2 * (2h) = pi * (r^2/4) * 2h = 0.5 * pi * r^2 * h. V2 = pi * r^2 * h. Thus V1 = 0.5 * V2.

AI explanation

The volume of a cylinder is given by V = pi * r^2 * h. Let the dimensions of C2 be radius r and height h, making its volume pi * r^2 * h. Since C1 has double the height and half the radius, its dimensions are height 2h and radius r/2, so its volume is pi * (r/2)^2 * 2h, which simplifies to pi * (r^2/4) * 2h, equaling (1/2) * pi * r^2 * h. Therefore, the volume of C1 is one half times the volume of C2.

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