Question

समान ऊंचाई वाले दो बेलनों की त्रिज्याउं में 2: 3 का अनुपात है तो उनके आयतनों में क्या अनुपात होगा ?​

Answer 1

Step-by-step explanation:

Let the volumes of both cylinders be $V_1 \: and \: V_2$

Heights of both the cylinders be h and their radii be 2r and 3r respectively.

Hence, volume of first cylinder

$V_1= \pi (2r)^2 h\\</p><p>\implies V_1= 4\pi r^2 h..... (1)$

Now, volume of second cylinder

$V_2= \pi (3r)^2 h\\</p><p>\implies V_2= 9\pi r^2 h..... (2)$

Dividing equation (1) by equation (2):

$\frac{V_1}{V_2} = \frac{4\pi r^2 h}{9\pi r^2 h}\\</p><p>\frac{V_1}{V_2} = \frac{4}{9}\\</p><p>\implies V_1: V_2 = 4 : 9$