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 ?

28 cm

We know that,

Volume of cylinder = πr²h

We have,

Volume ratio = 32 ∶ 9

Ratio of their heights is 8 ∶ 9

Area of the base of the second cylinder = 616 cm²

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

= Volume of second cylinder = 616 × 9y

Let the radius of first cylinder be r

= base area of first cylinder = πr²

Volume of first cylinder = πr² × 8y

Their ratios = 616 × \(\frac{9y}{(πr^2 × 8h) }\) = \(\frac{9}{32}\) 

=  (22r² × 8) ×\(\frac{1}{(616 × 9 × 7)}\) = \(\frac{32}{9}\) 

= r² = (616 × 9 × 32 × 7) ×\(\frac{1}{(9 × 22 × 8)}\) 

= r = 28