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Surface Areas and Volumes

Short Answer Type

161. A hollow cylindrical copper pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of copper used in making the pipe.

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162.

A powder tin has a square base with side 8 cm and height 13 cm. Another is cylindrical with the radius of its base 7 cm and its height 15 cm.

Find the difference in their capacities. $open parentheses Use space straight pi space equals 22 over 7 close parentheses$

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163. Coins of same size are placed one above the other and a cylindrical solid block is formed. The volume of this block is 49.28 cm³. Diameter of each coin is 2.8 cm and thickness 0.2 cm. Find the number of coins arranged in the block.

open parentheses straight pi equals 22 over 7 close parentheses

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164. The area of the base of a right circular cylinder is 15400 cm² and its volume is 92400 cm³. Find the height of the cylinder and also find curved surface of the cylinder.

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165.

A square piece of paper of side 22 cm is rolled to form a cylinder. Find the volume of the cylinder.

$open parentheses Take space straight pi space equals 22 over 7 close parentheses$

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166. A cylindrical container of base radius 28 cm contains sufficient water to submerge a rectangular block of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of water, when the block is completely submerged.

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167. A river 4 m deep and 60 m wide is flowing at the rate of 0.31 km/hour. How much water will fall into the sea in a minute?

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168. A rectangular piece of paper is 22 cm long and 12 cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder.

$open parentheses Use space straight pi equals 22 over 7 close parentheses$

When the rectangular piece of paper is rolled along its length, then the length of the piece forms the circumference of the base and the breadth of the piece becomes the height of the cylinder.
Let the base radius and height of the cylinder be r cm and h cm respectively.
Then,

$therefore space straight r space equals space 22$

$rightwards double arrow space space space space space space space space space space space space 2 cross times 22 over 7 cross times straight r equals 22 rightwards double arrow space space space space space space space space space space space space straight r equals 7 over 2 space cm space space space space space space space space space space space straight h space equals space 12 space cm$

$therefore$ Volume of the cylinder = $πr squared straight h$

= $22 over 7. open parentheses 7 over 2 close parentheses squared space left parenthesis 12 right parenthesis$
= 462²

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169. A well with 10 m inside diameter is long 14 m deep. Earth taken out of it is spread all around it to a width of 5 m to form an embankment. Find the height of the embankment.

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170. What is the mass of a metallic hollow cylindrical pipe 24 cm long with internal diameter 10 cm and made up of metal 5 mm thick. Density of the metal is 7 g per cm³.

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