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It costs र 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of र 20 per m², find
(i) inner curved surface area of the vessel,
(ii) radius of the base,
(iii) capacity of the vessel.

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156. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

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157. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

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158.

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, how much soup the hospital has to prepare daily to serve 250 patients?

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159. The volume of a cylinder is 448π cm³ and height 7 cm. Find its lateral surface area and total surface area.

Let the radius of the base of the cylinder be r cm.
h = 7 cm
Volume = 448 $straight pi$ cm³

$rightwards double arrow space space space space space space space space space πr squared straight h equals 448 straight pi rightwards double arrow space space space space space space space space space straight r squared straight h equals 448 rightwards double arrow space space space space space space space space space straight r squared left parenthesis 7 right parenthesis space equals space 448 rightwards double arrow space space space space space space space space space straight r squared equals 448 over 7 rightwards double arrow space space space space space space space space straight r squared equals 64 rightwards double arrow space space space space space space space space straight r equals square root of 64 rightwards double arrow space space space space space space space space straight r equals 8 space cm$

$therefore$ Lateral surface area = 2 $straight pi$ rh

$equals 2 cross times 22 over 7 cross times 8 cross times 7 equals 352 space cm squared$
Total surface area = $2 πr left parenthesis straight h plus straight r right parenthesis$

$equals 2 cross times 22 over 7 cross times 8 cross times left parenthesis 7 plus 8 right parenthesis$
$equals 2 cross times 22 over 7 cross times 8 cross times 15 equals 5280 over 7 cm squared equals 754.28 space space cm squared.$

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160. The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area and (iii) volume.

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