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.

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(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.

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(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.

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(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.

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

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(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.

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(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.

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(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).

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(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.

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(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.

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

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

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(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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