Question

The radii of two cylinders are in the ratio of 2:3 and
their heights are in the ratio of 5:4. Find the ratio of
their volumes.​

Answer 1

Given :-

• The radii of two cylinders are in the ratio of 2:3.
• Their heights are in the ratio of 5:4.

To Find :-

• Ratio of their volumes.

Solution :-

Given, The radii of two cylinders are in the ratio of 2:3.

⭐ Radius of 1st cylinder (r1) = 2

⭐ Radius of 2nd cylinder (r2) = 3

Given, Their heights are in the ratio of 5:4.

⭐ Height of 1st cylinder (h1) = 5

⭐ Height of 2nd cylinder (h2) = 4

Now,

⭐ Ratio of volume = Volume of 1st cylinder / Volume of 2nd cylinder

↪ V = π(r1)²h1 / π(r2)²h2

[ Putting values ]

↪ V = π(2)² × 5 / π(3)² × 4

↪ V = π × 4 × 5 / π × 9 × 4

↪ V = 20 π / 36 π

↪ V = 20/36

↪ V = 20 : 36

Hence,

• The ratio of their volumes is 20 : 36.