Q14 of 24 Page 227

The ratio of the lengths of the base radii of a right circular cylinder and a right circular cone is 3:4 and the ratio of their heights is 2:3; let us write the ratio of the volumes of the cylinder and the cone.

Let, base radius of the cone = 4r


Base radius of the cylinder = 3r


Let, the height of the cone = 3h


The height of the cylinder = 2h


∴ volume of the cone,


= 1/3 × π × (4r)2 × 3h


= 16πr2h


∴ volume of the cylinder,


= π × (3r)2 × 2h


⇒ 18πr2h


∴ ratio of the volumes of the cylinder and the cone,


= (16πr2h) ∶ (18πr2h)


= 8 ∶ 9


More from this chapter

All 24 →
14

The height of a right circular cone is 12cm. and its volume is 100 π cm3. Let us write the length of the radius of the cone.

 14

The curved surface area of a right circular cone is √5 times of its base area. Let us write the ratio of the height and the length of a right circular cone are always the three sides of a right-angled triangle.

 14

If the volume of a right circular cone is V cubic unit, base area A sq. unit and height is H unit, then let us write the value of .

 14

The numerical values of the volume and the lateral surface area of a right circular cone are equal. If the height and the radius of the cone are h unit and r unit respectively, then let us write the value of .