Question

the diameter of two cylinder are in the ratio 3 ratio 4 find the ratio of height if the volume is same​

Answer 1

Given -

• Diameter of two cylinders are in ratio 3:4.

• Their volumes are same.

To find -

• Their ratio of height.

Solution -

Let r be the radius of 1st cylinder and R be the radius of 2nd cylinder.

Let h be the Height of 1st cylinder and H be the Height of 2nd cylinder.

Now,

Diameter of 1st cylinder/ Diameter of 2nd cylinder = 3/4

→ 2πr/2πR = 3/4

→ r/R = 3/4

Now,

Volume of 1st cylinder/Volume of 2nd cylinder = 1

→πr²h/πR²H = 1

→ r²h/ R²H = 1

→ (r²/R²) (h/H) = 1

→ (3/4)² (h/H) = 1

→(9/16) (h/H) = 1

→(H/h) = 9/16

$\implies$ H : h = 9 : 16

$\therefore$ The ratio of their height is 9 : 16

______________________________________

Answer 2

Step-by-step explanation:

Given -

• Diameter of two cylinders are in ratio 3:4.

• Their volumes are same.

To find -

• Their ratio of height.

Solution -

• Let r be the radius of 1st cylinder and R be the radius of 2nd cylinder.

Let h be the Height of 1st cylinder and H be the Height of 2nd cylinder.

Now,

Diameter of 1st cylinder/ Diameter of 2nd cylinder = 3/4

→ 2πr/2πR = 3/4

→ r/R = 3/4

Now,

Volume of 1st cylinder/Volume of 2nd cylinder = 1

→πr²h/πR²H = 1

→ r²h/ R²H = 1

→ (r²/R²) (h/H) = 1

→ (3/4)² (h/H) = 1

→(9/16) (h/H) = 1

→(H/h) = 9/16

$\implies$ H : h = 9 : 16

$\therefore$ The ratio of their height is 9 : 16

______________________________________