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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.

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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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347. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

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348. Find the volume of a sphere whose surface area is 55.44 cm². $open parentheses straight pi equals 22 over 7 close parentheses$

Let the radius of the sphere be r cm.
Then,
4πr² = 55.44
$rightwards double arrow space space 4 cross times 22 over 7 cross times r squared equals 55.44 rightwards double arrow space space space space space space space space r squared equals fraction numerator 55.44 cross times 7 over denominator 4 cross times 22 end fraction equals 4.41 rightwards double arrow space space space space space space space space r equals square root of 4.41 end root equals 2.1 space c m space space space space$

$therefore$ Volume of the sphere = $4 over 3 πr squared$

$equals 4 over 3.22 over 7 left parenthesis 2.1 right parenthesis cubed$
= 38.808 cm³