Question

The ratio of the radius of base and height of a cylinder is 3:7. If its volume is 1584 cm³, then find the radius and height of the cylinder.

Answer 1

Given:

Ratio of radius to height of the cylinder = 3:7

Volume of the cylinder = 1584 cm³

To find:

Radius and height of the cylinder

Step 1: Assume radius and height

r = 3x cm, h = 7x cm

Step 2: Use the formula for volume of a cylinder

Volume = πr2h

Substitute the values:

1584 = π(3x)² (7x)

1584 = π × 9x² × 7x

1584 = 63πx³

Step 3: Substitute π = `22/7`

1584 = 63 × `22/7 x^3`

1584 = 198x³

Step 4: Solve for x

`x^3 = 1584/198 = 8`

x = 2

Step 5: Find radius and height

r = 3x = 3 × 2 = 6 cm

h = 7x = 7 × 2 = 14 cm