Mensuration Made Great : With Word Problems For Class 8th,9th,10th

Q.1) Find the number of coins, each of radius 0.75cm and thickness of 0.2cm, that should be melted to make a right circular cylinder of height 8cm and base of radius 3cm.

SOLUTION:

Given: COINS RIGHT CIRCULAR CYLINDER

Radius = r = 0.75cm Height = 8cm
Thickness = h = 0.2cm Radius = r = 3cm

No. of coins = ?

STEP – 1) Volume of coins = pie * r ² * h
= 22 / 7 * 0.75 * 0.75 * 0.2

STEP – 2) Volume of right circular cylinder = pie * r ² * h
= 22 / 7 * 3 * 3 * 8

STEP – 3) No. of coins = Volume of circular cylinder / Volume of coins
= 22 / 7 * 3 * 3 * 8 / 22 / 7 * 0.75 * 0.75 * 0.2
= 3 * 3 * 8 * 100 * 100 * 10 / 75 * 75 * 2
= 8 * 4 * 2 * 10
= 640 coins
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Q.2) A rectangular sheet of paper with dimensions 154cm by 10cm is folded along its length. Find the volume of the hollow cylinder so generated.

SOLUTION: RECTANGULAR SHEET PAPER

Given:
Length = L = 154cm
Breadth = B = 10cm
Volume of hollow cylinder = ?

STEP – 1) Length of rectangular sheet = Circumference = 2 * pie * r
= 154 = 2 * 22 / 7 * r
= 49 / 2
R = 49 / 2

STEP – 2) Volume of hollow cylinder = pie * r² * h
= 22 / 7 * 49 / 2 * 49 / 2 * 70
= 77 * 49 * 5
= 18, 865 cm³
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Q.3) The diameter of two cylinders are in the ratio 3 : 4. Find the ratio of their heights if their volumes are equal ?

SOLUTION: TWO CYLINDERS

Given:
Diameter of two cylinders = 3 : 4
Volume of 1^st cylinder = Volume of 2^nd cylinder
Diameter of 1^st cylinder = 3x Radius of 1^st cylinder = 3x / 2
Diameter of 2^nd cylinder = 4x Radius of 2^nd cylinder = 4x / 2

Volume of 1^st cylinder = Volume of 2^nd cylinder
pie * r²₁ * h₁ = pie * r²₂ * h²₂
pie * ( 3x / 2 )² * h₁ = pie * ( 4x / 2 )² * h²₂
9x² / 4 * h₁ = 16x² / 4 * h₂
h₁ / h₂ = 16x² / 4 * 4 / 9x²
h₁ / h₂ = 16 / 9

ANS: Ratio of heights of two cylinders is 16 : 9
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Q.4) 1m³ of ice weighs 700 kg. What is the weight of a block of ice with dimensions 0.75m * 0.25m * 0.15m ?

SOLUTION: ICE BLOCK

Given:
1m³ of ice weighs = 700 kg
Length = L = 0.75m
Breadth = B = 0.25m
Height = H = 0.15m

Volume of ice block = L * B * H
= 0.75 * 0.25 * 0.15

STEP – 1) Volume = 0.028125m³

STEP – 2) 1m³ —- weighs 700 kg
0.028125m³ —- weighs 700 kg

Weight of a block of ice = 0.028125 * 700
= 19.6875 kg
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Q.5) A road roller takes 750 complete revolutions to level a road . Find the area of the road if the diameter of the roller is 98cm and its length 1.5m.

SOLUTION: ROAD ROLLER

Given:
No. of revolutions = 750
Diameter = d = 98cm
Radius = r = 98 / 2 = 49cm
Length = L = 1.5m = 1.5 * 100 = 150cm
Area of road roller = ?

STEP – 1) CSA of road roller = 2 * pie * r * h
= 2 * 22 / 7 * 49 * 150
= 46, 200 cm³

STEP – 2) Area of road roller = CSA of road roller * No. of revolutions
= 46200 * 750
= 34,650,000 cm³
= 34650000 / 100 * 100 ( 1m² = 10000cm )
= 3465 m³
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