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Surface Areas and Volumes

Short Answer Type

341. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

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342. Find the volume of a sphere whose surface area is 154 cm².

Let the radius of the sphere be r cm. Surface area = 154 cm²

rightwards double arrow

rightwards double arrow space space space space space space space space space space space space space space space space space space space space 4 πr squared equals 154 rightwards double arrow space space space space space space space space space space space space space space space 4 cross times 22 over 7 cross times straight r squared equals 154 rightwards double arrow space space space space space space space space space space space space space space space straight r squared equals fraction numerator 154 cross times 7 over denominator 4 cross times 22 end fraction rightwards double arrow space space space space space space space space space space space space space space space straight r squared equals 49 over 4 space space space space space space space space rightwards double arrow space straight r equals square root of 49 over 4 end root rightwards double arrow space space space space space space space space space space space space space space straight r equals 7 over 2 space cm

therefore

Volume of the sphere =

4 over 3 πr cubed

equals 4 over 3 cross times 22 over 7 cross times open parentheses 7 over 2 close parentheses cubed equals space 539 over 3 space cm cubed equals 179 2 over 3 space cm squared

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343.

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of र 498.96. If the cost of white-washing is र2.00 per square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome.

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344.

Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the

(i) radius r´ of the new sphere,
(ii) ratio of S and S’.

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345. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

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346. If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume, what is the diameter of the sphere?

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