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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.

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

Let the base radius and height of the cylinder be r cm and h cm respectively.

Then,

   $space space space space space space space space space 2 πr equals 22 rightwards double arrow space space space 2 cross times 22 over 7 cross times straight r equals 22 rightwards double arrow space space space space straight r equals 7 over 2 space cm space space space space space space space space straight h space equals space 22 space cm$
$therefore$ Volume of the cylinder = $πr squared straight h$

   $equals 2.22 over 7.7 over 2.7 over 2.22 equals space 847 space cm cubed$

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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

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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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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

165.
A square piece of paper of side 22 cm is rolled to form a cylinder. Find the volume of the cylinder.

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