Question

the radii of two cylinders are in the ratio 2:3 and their height are in the ratio 5:3 .calculate the ratio of their curved surface areas.

Answer 1

let 2x and 3x be the radii of the two cylinders
and their height be 5y and 3y respectively

now
C.S.A of first cylinder (a) = 2 × 22/7 × 2x × 5y
C.S.A of second cylinder (b) = 2 × 22/7 × 3x × 3y
ratio of them = a/b
= (2 × 22/7 × 2x × 5y)/(2 × 22/7 × 3x × 3y)
= 10xy / 9xy
= 10/9
therefore their C.S.A are in the ratio 10/9

Answer 2

Answer:

Ratio of CSA=10/9 AND Ratio of Volume=20/27

Step-by-step explanation:

Let the radii of the cylinders be 2x and 3x respectively.

And let their heights be 5y and 3y respectively.

CSA of 1st cylinder=2πrh=2π×2x×5y

CSA of 2nd cylinder=2πRH=2π×3x×3y

∴Ratio of CSA of the 2 cylinders=2π×2x×5y÷2π×3x×3y

                                                     =10xy÷9xy

                                                     =10/9

Volume of 1st cylinder= πr²h=π×4x²×5y

Volume of 2nd cylinder= πR²H=π×9x²×3y

∴Ratio of the volume of the 2 cylinders=π×4x²×5y÷π×9x²×3y

                                                                =4×5÷9×3=20÷27=20/27