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14. Surface Areas and Volumes
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Q3 of 44 Page 14

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm, and the diameter of the capsule is 5 mm. Find its surface area.


Given:


Diameter of cylinder = 5mm


The radius of cylinder


Height of cylinder = 14 – 5 = 9mm


Here, Diameter of hemisphere =. 5mm


So,


The total area of the capsule = CSA of cylinder + CSA of 2 hemispheres


= 2πrh + 2×2πr2




=220 mm2


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1

A toy is in the form a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. Find the volume of the toy.

2

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm, and the height of the cone is 4 cm. The solid is place in a cylindrical tub full of water in such a way that the whole solid is submerged in water left in the tub.

4

A room in the form of a cylinder, surmounted by a hemispherical vaulted dome, contains m3 of air and the internal diameter of the building is equal to the height of the crown of the vault above the floor. Find the height

5

The interior of a building is in the form of a cylinder of diameter 4.3 m and height 3.8 m surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and the volume of the building. [Take π=3.14]

Questions · 44
14. Surface Areas and Volumes
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