WORD PROBLEMS RELATED TO
MENSURATION
CLASS 8TH, 9TH & 10TH
Q.1) Find the volume of the right circular cylinder whose curved surface area is 2640 cm2 and
the circumference of the base is 66 cm.
SOLUTION: circular cylinder
Given : Curved surface area = LSA = 2640 cm2
Circumference = C = 66 cm
Find : Volume = V = ?
Step 1). Circumference = C = 2*pie*r
66 = 2*22/7*r
66*7/22*1/2= r
21/2 cm = r
Step 2). LSA = 2*pie*r*h
2640= 2 * 22/7 * 21/2 * h
2640 * 1/2*7/22*2/21 =h
40cm=h
Step 3). Volume = V = pie * r2 * h
V = 22/7 * 21/2 * 21/2 *40
= 13860cm2
Ans : The volume of the right circular cylinder is 13860cm2.
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Q.2) The ratio of the surface area of two cubes is 16 : 49. Find the ratio of their volumes.
SOLUTION: Two cubes
Given : Ratio of their surface areas = 16 :49
Find : Ratio of their volumes = ?
Step 1) Ratio of their surface areas = 16 / 49
6 * a2 of the 1st cube / 6 * a2 of the second cube =16 /49
a2 of the first cube / a2 of the second cube = 16 /49
a of the first cube / a of the second cube = 4/7
Step 2). Volume of the first cube / Volume of the second cube =
= a3 of the first cube / a3 of the second cube
= 43 / 73 = 64/343
Ans : The ratio of their volumes is 64 :343.
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Q3) A Water tank is 1.4m long, 1m wide and 0.7m deep. How many litres of water can it hold?
SOLUTION : Water tank ( cuboidal)
Given : Length = L = 1.4m wide = B = 1m deep = H = 0.7m
Find : How many litres of water it can hold = volume = ?
V = L * B * H
= 1.4 * 1 * 0.7
= 0.98 m3
= 0.98 * 1000 ( 1m3 = 1000 L )
980 L
Ans : It can hold 980 L of water.
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Q.4) Water from a cylindrical water tank of height 10.5m and a base with diameter 4.2m is emptied into a cuboidal water tank of dimensions 15m * 7m * 6m. Find the height of water in the cuboidal water tank ?
SOLUTION: CYLINDRICAL TANK
Given: ( STEP – 1 )
Height = h = 10.5m
Diameter = d = 4.2m
Radius = r = 4.2 / 2 = 2.1m
Volume of cylinder = pie * r2 * h
= 22 / 7 * 2.1 * 2.1 * 10.5
= 22 / 7 * 21 / 10 * 21 / 10 * 105 / 10
= 14553 / 100
= 145.53 m2
CUBOIDAL TANK
Given: ( STEP – 2 )
Length = L = 15m
Breadth = B = 7m
Height = H = 6m
Area of the base of cuboidal tank = L * B
= 15 * 7
= 105 m
( STEP – 3 )
Height of water in cuboidal tank = Volume of cylindrical tank / Base area of cuboidal tank
= 145.53 / 105
= 1.386 m
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Q.5) A circular pit with diameter 1.5m is dug to a depth of 21m. What is the volume of the earth dug out ?
SOLUTION: CIRCULAR PIT
Given:
Diameter = d = 1.5m
Radius = r = 1.5 / 2 m
Depth = height = h = 21m
Volume of the earth dug out = ?
Volume of the earth dug out = Volume of circular pit = pie * r2 * h
= 22 / 7 * 1.5 / 2 * 1.5 / 2 * 21
= 37.125 m3
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Q.6) A rectangular sheet of a paper is folded about its width 15cm. If the length of the sheet is 22cm, find the volume of hollow cylinder thus formed ?
SOLUTION: RECTANGLUAR SHEET PAPER
Given:
Folded by width = Circumference of hollow cylinder = 15cm
Length = Height of the hollow cylinder = 22cm
Volume of the hollow cylinder = ?
( STEP – 1 )
Circumference = 2 * pie * r
15 = 2 * 22 / 7 * r
15 / 2 * 7 / 22 = r
2.386 cm = r
( STEP – 2 )
Volume of hollow cylinder = pie * r2 * h
= 22 / 7 * 2.386 * 2.386 * 22
= 2755.41 / 7
= 393.630009
= 393.65 cm3
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Q.7) A river 10m deep and 100m wide is flowing at the rate of 7.5 km / hr. Find the quantity of water that runs into the sea per second ?
SOLUTION: RIVER
Given:
Height of the river = h = 10m
Breadth = b = 100m
Rate of flowing = Speed = 7.5 km / hr.
Quantity of water = Volume = ?
Length of the river = Distance = ?
( STEP – 1 )
Speed = Distance / Time
= 7.5 km / 1 hour
= 7.5 * 1000m / 3600 sec
= 7500 / 3600
= 25 / 12 m
Distance = Length of the river = 25 / 12 m
( STEP – 2 )
Volume = L * B * H
= 25 / 12 * 100 * 10
= 25000 / 12
= 2083.33m3
ANS: The quantity of water that runs into the sea per second is 2083.33m3
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