Question

Two cylindrical jars have their diameters in the ratio 3:1, the height 1:3. Then the ratio of their volumes is

(a) 1 : 4

(b) 1 : 3

(c) 3 : 1

(d) 2 : 5

Answer 1

Ratio in the diameters of two cylinder = 3:1

and ration in their heights = 1:3

Let radius of the first cylinder $\left(r_1\right)$ = 3x

and radius of second $\left(r_2\right)$ = x

and height of the first $\left(h_1\right)$ = y

and height of the second $\left(h_2\right)$ =3y

Now volume of the first cylinder = $\pi r^2$ h

=$\pi (3x{)}^2\times y=9\pi x^2$ y

and of second cylinder = $\pi \left(x^2\right)$ (3y) =$3\pi x^2$ y

$\therefore$ Ration between then = $9\pi x^{2}y:3\pi x^2$ y

= 3:1

Hence correct answer will be (c) 3 : 1