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151. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1l)

Let the base radius of the cylindrical vessel be r cm.
Then, circumference of the base of the cylindrical vessel = 2πr cm.
According to the question,

$rightwards double arrow space space space 2 cross times 22 over 7 cross times straight r equals 132 rightwards double arrow space space space straight r equals fraction numerator 132 cross times 7 over denominator 2 cross times 22 end fraction$

$rightwards double arrow$ r = 21 cm; h = 25 cm

∴ Capacity of the cylindrical vessel = $πr squared straight h$

$equals 22 over 7 left parenthesis 21 right parenthesis squared space left parenthesis 25 right parenthesis space cm cubed equals space 34650 space cm cubed equals 34650 over 1000 l italic equals italic space italic 34 italic. italic 65 italic space l$

Hence, the cylindrical vessel can hold 34.65 l of water.

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152. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³of wood has a mass of 0.6 g.

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153.

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g

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154.

If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find (i) radius of its base (ii) its volume. (Use

straight pi

= 3.14)

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155.

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.

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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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