Question

Two cylindrical cans have bases of the same size. The diameter of each is 14 cm. One of the cans is 10 cm high and the other is 20 cm high. The ratio of their volumes is

Answer 1

volume of cylinder = πr^2h

radius of both will be same = 7cm

height of first = 10cm (h)

height of second = 20 cm (H)

ratio of volume of second to first = πr^2H/ πr^2h = H /h

20/10= 2:1

ratio of first to second = h/H

10/20= 1:2

Answer 2

$\huge\mathcal{\underline\purple{Answer}:-}$

$\fbox\green{Given~:}$

Two cylindrical cans have bases of the same size. The diameter of each is 14 cm. One of the cans is 10 cm high and the other is 20 cm high.

$\fbox\blue{To~Find~:}$

The ratio of their volumes .

$\fbox\pink{Solution~:}$

Let the dimensions of the two cans be as under :

Can I :

• Radius = $r1 = 7cm$

• Height = $h1= 10cm$

• Volume = $v1 = ?$

Can II :

• Radius = $r2 = 7cm$

• Height = $h2= 20cm$

• Volume = $v2 = ?$

Then ,

$v1 = πr1²h1 = π x 7² x 10 cm³ = 490πcm³$

$v2= πr2²h2 = π x 7² x 20 cm³ = 980πcm³$

•°• $The~ Ratio~ of ~their ~volumes =\frac{v1}{v2} = \frac{490\pi}{980\pi} = \frac{1}{2}$

$\fbox\red{•°• Ratio~of~their~volumes = 1:2}$