VOLUME OF CYLINDERS SPHERES AND CONES WORD PROBLEMS

(1)  Find the volume of a solid cylinder whose radius is 14 cm and height is 30 cm.

Solution

(2)  A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, then find the quantity of soup to be prepared daily in the hospital to serve 250 patients?

Solution

(3)  The sum of the base radius and the height of a solid cylinder is 37 cm. If the total surface area of the cylinder is 1628 sq.cm, then find the volume of the cylinder.

Solution

(4)  Volume of a solid cylinder is 62.37 cu.cm. Find the radius if its height is 4.5 cm.

Solution

(5)  The radii of two right circular cylinders are in the ratio 2:3. Find the ratio of their volumes if their heights are in the ratio 5:3.

Solution

(6)  The radius and height of two circular cylinders are in the ratio 5 : 7. If its volume is 4400 cu.cm, find the radius of the cylinder.

Solution

(7)  A rectangular sheet of metal foil with dimension 66 cm x 12 cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder.

Solution

(8)  A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil.

Solution

(9)  Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume.

Solution

(10)  The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.

Solution

(11)  A vessel is in the form of frustum of a cone. Its radius at one end and the height are 8 cm and 14 cm respectively. If its volume is 5676/3 cm³, then find the radius at the other end.

Solution

(12)  The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π cm. If the depth is 14 cm, then find its volume.

Solution

(13)  A right angled triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the fixed side of 12 cm. Find the volume of the solid generated.

Solution

(14)  The radius and height of a right circular cone are in the ratio 2:3. Find the slant height if its volume is 100.48 cu.cm (take Π = 3.14).

Solution

(15)  The volume of a cone with circular base is 216 Π cu.cm. If the base radius is 9 cm, then find the height of the cone.

Solution

(16)  Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 g/cm³. (Mass = Volume x Density).

Solution

(17)  The outer and inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume.

Solution

(18)  The volume of a solid hemisphere is 1152 Π cu.cm. Find its curved surface area.

Solution

(19)  Find the volume of the largest right circular cone that can be cut of a cube whose edge is 14 cm.

Solution

(20)  The radius of a spherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

Solution

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