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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

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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.

Radius of the wall

(r) =

10 over 2 straight m equals 5 space straight m

Depth of the wall (h) = 10 m Volume of the earth dug out = Volume of the well = π r²h = π(5)²(10) = 250π m³ Radius of the well with embankment (R)
= 5 + 5 = 10 m π Area of the embankment
= Area of the well with embankment
– Area of the well without embankment = πR² – πr² = π(R + r) (R – r)
= π(10 + 5) (10 – 5)
= 75π m²∴ Height of the embankment

$equals fraction numerator Volume space of space the space earth space dug space out over denominator Area space of space the space embankment end fraction$

$equals fraction numerator 250 straight pi over denominator 75 straight pi end fraction equals 10 over 3 space straight m$

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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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