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The radii of the two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Find the ratio of their volumes.

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\frac{15}{27}

\frac{25}{27}

\frac{30}{27}

answer is A.

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Detailed Solution

It is given that the ratio of the radii of the two cylinders is 2:3.
We are also given that the ratio of their heights is 5:3.
Assume that the cylinders are one with radius and height

and

and the other with radius and height,

and

respectively.

So, as we are given that the ratio of the radii is 2:3, we can say that,

⇒ r R = 23 → (1)

As we are given that the ratio of heights of cylinders is 5:3, we can say that,

⇒ h H = 53 → (2)

Now let us consider the formula for volume of the cylinder.

Volume = π × Radius 2 × Height

Using this formula, we get the volume of first cylinder as,

⇒ Volume = π r 2 h

Using the above formula, we get the volume of second cylinder as,

⇒ Volume = π R 2 H

Now let us consider the ratio of volumes of the cylinders.

⇒ π r 2 h π R 2 H ⇒ r 2 R 2 × h H ⇒ r R 2 × h H

Using equations (1) and (2) we can write the above ratio as,

⇒ 232 × 53 ⇒ 49 × 53 ⇒ 2027

Hence, the ratio of volumes of the two cylinders as

2027

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