In what ratio are the volumes of a cylinder, a cone and a sphere, if e

1.	In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same heightA) 1 : 3 : 2 B) 2 : 3 : 1 C) 3 : 1 : 2 D) 3 : 2 : 1
Answer» Correct option is: C) 3 : 1 : 2 Let 2r be the diameter of cylinder, cone of sphere. \(\therefore\) Height of sphere = 2r Then height of cone = Height of cylinder = 2r. Now, \(V_1 : V_2 : V_3\) = Volume of cylinder : Volume of cone : Volume of sphere = \(\pi r^2h : \frac 13 \pi r^2 h : \frac 43 \pi r^3\) (\(\because\) h = 2r) = \(2 \pi r^3 : \frac {2 \pi r^3 }{3} = \frac {4 \pi r^3 }{3}\) = 2 : \(\frac 23 : \frac 43\) (On dividing by \(\pi r^3 \)) = 6 : 2 : 4 (On multiplying by 3) = 3 : 1 : 2 (On dividing by 2) Hence, the ratio of their volumes is 3 : 1 : 2. Correct option is: C) 3 : 1 : 2

In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same heightA) 1 : 3 : 2 B) 2 : 3 : 1 C) 3 : 1 : 2 D) 3 : 2 : 1

Answer»

Correct option is: C) 3 : 1 : 2

Let 2r be the diameter of cylinder, cone of sphere.

\(\therefore\) Height of sphere = 2r

Then height of cone = Height of cylinder = 2r.

Now, \(V_1 : V_2 : V_3\) = Volume of cylinder : Volume of cone : Volume of sphere

= \(\pi r^2h : \frac 13 \pi r^2 h : \frac 43 \pi r^3\) (\(\because\) h = 2r)

= \(2 \pi r^3 : \frac {2 \pi r^3 }{3} = \frac {4 \pi r^3 }{3}\)

= 2 : \(\frac 23 : \frac 43\) (On dividing by \(\pi r^3 \))

= 6 : 2 : 4 (On multiplying by 3)

= 3 : 1 : 2 (On dividing by 2)

Hence, the ratio of their volumes is 3 : 1 : 2.

Correct option is: C) 3 : 1 : 2