WORD PROBLEMS
RELATED TO MENSURATION
CLASS 8th, 9th AND 10th
Q.1) An open cylindrical box of height 20cm and diameter 21cm is to be made using a cardboard. Find the area of the cardboard required to make the box.
SOLUTION: OPEN CYLINDRICAL BOX
Given:
Height = 20cm
Diameter = 21cm
Radius = 21 / 2
Area of cardboard required = ?
Area of cardboard required = CS + Area of base
= 2 * pie * r * h + pie * r2
= pie * r ( 2h + r )
= 22 / 7 * 21 / 2 * ( 2 * 20 + 21 / 2 )
= 33 ( 40 +21 / 2)
= 33 ( 80 / 2 + 21 / 2 )
= 33 * 101 / 2
= 1666.5cm2
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Q.2) A hollow cylindrical carton having a curved surface area of 1372cm2 is cut along its height and laid flat into a rectangular sheet of width 28cm. Find the perimeter of the rectangular sheet thus obtained.
SOLUTION: HOLLOW CYLINDRICAL CARTON
Given:
CSA = 1372cm2
Width = Height = 28cm
Cut along its height and laid into rectangular sheet
Perimeter of rectangular sheet = P = ?
P = 2 ( L + B )
Length = L = ?
STEP – 1) CSA = 1372
2 * pie * r * h = 1372cm
2 * pie * r * 28 = 1372
2 * pie * r = 1372 / 28
2 * pie * r = 49
Circumference = 49cm
Circumference = Length of rectangular sheet = 49cm
STEP – 2) Perimeter of rectangular sheet = 2 ( L + B )
= 2 ( 49 + 28 )
= 2 * 77
= 154cm
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Q.3) A cylindrical perfume bottle of diameter 7cm has a silver metal lid of the same radius as its base and height of 2cm. The height of the bottle is 6cm. Find the surface area if the lid.
SOLUTION:
Given: CYLINDRICAL BOTTLE CIRCULAR LID
Diameter = 7cm Radius = 7 / 2cm
Radius = 7 / 2cm Height = 2cm
Height = 6cm SA of lid = ?
TSA of lid = CSA of lid + Area of top of the lid
=( 2 * pie * r * h) +( pie * r2)
= pie * r * ( 2 * h + r )
= 22 / 7 * 7 / 2 * ( 2 * 2 + 7 / 2 )
= 11 * ( 4 + 7 / 2 )
= 11 * ( 8 / 2 + 7 / 2 )
= 11 * 15 / 2
= 82.5cm2
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Q.4) How many cubes of side 30cm can be out from a solid cuboid whose length is 3m, breadth 1.5m and height 60cm ?
SOLUTION: CUBES SOLID CUBOID
Given: Side = 30cm Length = L = 3m = 300cm
Breadth = B = 1.5m = 150cm
Height = H = 60cm
No. of cubes can be cut from a solid cuboid = ?
STEP – 1) Volume of cubes = a3
= 30 * 30 * 30 cubic cm
STEP – 2) Volume of cuboid = L * B * H
= 300 * 150 * 60 cubic cm
STEP – 3) No. of cubes = Volume of cuboid / Volume of cube
= 300 * 150 * 60 / 30 * 30 * 30
= 100 cubes
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Q.5 ) A cuboidal water tank contains 24000L of water. The tank is 6m long and 3.5 m wide. Find the height of the water in the tank.
SOLUTION:
Given: CUBOIDAL WATER TANK TANK
Volume of water = 24000L Length = L = 6m
Width = Breadth = 3.5m
STEP – 1) Volume of water = 24000L
= 24000 / 1000
= 24m3 ( 1m3 = 1000L )
STEP – 2) Volume of the water = Volume of the tank
24 = L * B * H
24 = 6 * 3.5 * H
24 / 6 * 3.5 = H
8 / 7 = H
1.142 m = H
ANS: The height of the water in the tank is 1.142 m.
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