Question

two right circular cylinders of equal heights have their radii in the ratio 2:5 . Find the ratio of their curved surface area and the ratio of their volumes.

Answer 1

HEY THERE!

$\bf{\bold{Proper \: \: Question:-}}$

radii of two cylinder are in the ratio 2 : 3 and their height are in 5 : 3 .Calculate the ratio of their volume and the ratio of curved surface.

$\bf{\bold{Method \: \:Of \: \: Solution:-}}$

Let the radii be 2r, 3r of two Cylinder!

Let the height be 5h and 3h!

Then, Using Formula of Volume!

Volume = πr²h

Thus, According to the Question Statement!

Volume = πr²h /πr²h

Volume = π×(2r)² × (5h) / π ×(3r)² × 3h

Volume. = 4r²×5h/9r²×3h

Volume = 4×5 /9×3

•°• Volume = 20/27

Now, Find the Ratio of curved Surface!

Formula of Curved Surface = 2πrh

Substitute the Given value in Formula Equation!

In Ratio,Formula of Curved Surface = 2πrh/2πrh

Curved Surface= 2×π ×2r ×5h /2×π×3r×3h

Curved Surface = 2×5 /9

Curved Surface = 10/9

Therefore, the ratio of their volume and the ratio of curved surface respectively 20:27 and 10:9 respectively.

Answer 2

Volume =) πr²h /πr²h

Volume =) π×(2r)² × (5h) / π×(3r)² ×3h

Volume =) 4r²×5h/9r²×3h

Volume =)4×5 /9×3

Volume =) 20/27

So, Volume = 20:27

Formula of Curved Surface = 2πrh




Curved Surface=) 2×π×2r×5h /2×π×3r×3h

Curved Surface =) 2×5 /9

Curved Surface =) 10/9

So Surface = 10:9