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

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

A.

20:27

B.

27:20

C.

4:9

D.

9:4

Correct option is A

Given:
Ratio of radii of two cylinders is 2:3.
Ratio of heights of two cylinders is 5:3.

Formula Used:
Volume of a cylinder = πr2h\pi r^{2}h​​

Solution:
Let the radii of the two cylinders be:

r1=2xr2=3xr_{1}=2x\\r_{2}=3x​​

Let the heights of the two cylinders be:
h1=5yh2=3yh_{1}=5y\\h_{2}=3y​​
The ratio of their volumes is given by:
V1V2=πr12h1πr22h2\frac{V_{1}}{V_{2}}=\frac{\pi r_{1}^{2}h_{1}}{\pi r_{2}^{2}h_{2}}​​
Substitute the values into the formula:
V1V2=π(2x)2(5y)π(3x)2(3y)\frac{V_{1}}{V_{2}}=\frac{\pi(2x)^{2}(5y)}{\pi(3x)^{2}(3y)}​​
Simplify the expression:
V1V2=4x2×5y9x2×3y\frac{V_{1}}{V_{2}}=\frac{4x^{2}\times5y}{9x^{2}\times3y}​​
Cancel out the common terms:
V1V2=2027\frac{V_{1}}{V_{2}}=\frac{20}{27}​​
The ratio of their volumes is 20:27.

Final Answer
So the correct answer is (a)

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