One cylindrical circle is 2 times higher than the second of the same circle shape, while the second is 1.5

One cylindrical circle is 2 times higher than the second of the same circle shape, while the second is 1.5 times wider than the first. It is necessary to determine the ratio of the volume of the cup V2 / V1.

Let’s write down the parameters of both mugs:

1) height h = 2 * h2; width, that is, the diameter of the base of the circle = d, volume v1.

2) height h2, width, diameter is 1.5 * d, volume v2.

Let’s calculate the volumes of the mugs.

v1 = 3.14 * d ^ 2/4 * 2 * h2.

v2 = 3.14 * (1.5 * d) ^ 2/4 * h2.

It remains only to divide v2 / v1 = [3.14 * (1.5 * d) ^ 2 * h2 / 3.14 * (d) ^ 2/4 * 2 * h2] = 2.25 d ^ 2 * h2 / d ^ 2 * 2 * h2 = 1.125.

That is, the volume of the second mug is not much larger than the volume of the first mug.