The ratio of the volume of first and second cylinder is 32 ∶ 9 and the ratio of their heights is 8 ∶ 9. If the area of the base of the second cylinder is 616 cm², then what will be the radius of the first cylinder? 

Given:

Volume ratio = 32 ∶ 9

Ratio of their heights is 8 ∶ 9

Area of the base of the second cylinder is 616 cm2

Concept Used:

Volume of cylinder = πr²h

Calculation:

Volume of the cylinder can be written as 32y and 9y

Height of the cylinder can be written as 8h and 9h

Since we know that the Volume of cylinder is Area of base × height

⇒ Volume of second cylinder = 616 × 9h

Let the radius of first cylinder be r

⇒ base area of first cylinder = πr²

Volume of first cylinder = πr² × 8h

Their ratios can be written as

⇒ 616 × 9h/ (πr² × 8h) = 9/32

Put π = 22/7

⇒  (22r2 × 8)/(616 × 9 × 7)/ = 32/9

⇒ r² = (616 × 9 × 32 × 7)/(9 × 22 ×  8)

⇒ r = 28

∴ Radius of first cylinder is 28 cm.

∴ Option 3 is the correct answer.