WORD PROBLEMS
RELATED TO MENSURATION
CLASS 8th, 9th, AND 10th
Q.1 ) Six solid cubical stools with edge 65cm are to be painted red on all the sides. Find the quantity of paint required to paint 6 cubical stools if one can of paint is required to paint 11,700cm2 of area.
SOLUTION:
Given:
No. of cubical stools = 6
Each edge = 65cm
One can of paint is required to paint 11,700cm2 of area
Total quantity of paint required for 6 stools = ?
STEP – 1) TSA of 1 cubical stool = 6a2
= 6 * 65 * 65
= 25,350cm2
STEP – 2) TSA of 6 cubical stools = 6 * 25,350
= 1,52,100cm2
STEP – 3) 1 can of paint —- Area painted 11700cm2
How many cans required —- Area to be painted 1,52,100
No. of cans required = 1,52,100 / 11,700
= 13 cans
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Q.2) Five cubes of side 3cm are joined together to form a cuboid. Find the surface area of the generated cuboid.
SOLUTION: 5 CUBES JOINED TO FORM CUBOID
Given:
No. of cubes = 5
Side of each cube = 3cm
Length of cuboid = 5 * 3
= 15cm
Breadth of cuboid = 3cm
Height of cuboid = 3cm
TSA of cuboid = 2 * ( LB + BH + HL )
= 2 *[( 15 * 3 ) + ( 3 * 3 ) + ( 3 * 15 )]
= 2 * ( 15 + 9 + 45 )
= 2 * 99
= 198cm2
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Q.3) A cylindrical roller with diameter 77cm and height 1m is used to level a rectangular park with dimensions 22m * 11m. Find the number of revolutions required to level the park.
SOLUTION: CYLINDRICAL ROLLER
STEP – 1) Diameter = 77cm
Radius = 77 / 2
Height = 1m = 100cm
CSA = 2 * pie * r * h
= 2 * 22 / 7 * 77 / 2 * 100
= 121 * 200
= 24200cm2
= 24200 / 100 * 100
= 2.42m2
( 1cm2 = 10000m2 )
STEP – 2 ) RECTANGULAR PARK
Given:
Length = L = 22m
Breadth = B = 11m
Area of park = L * B
= 22 * 11
= 242m2
STEP – 3) NO. OF REVOLUTIONS = ?
No. of revolutions = Area of park / CS Area of roller
= 242 / 2.42
= 24200 / 242
= 100 revolutions
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Q.4) The ratio of the curved surface area and the total surface area of right circular cylinder is 5:7. Find the ratio between the height and radius of the cylinder.
SOLUTION: RIGHT CIRCULAR CYLINDER
Given:
Ratio of CSA : TSA = 5 : 7
Ratio of H : R = ?
Curved SA / TSA = 5 / 7
2 * pie * r * h / 2 * pie *r * ( h + r ) = 5 / 7
h / ( h + r ) = 5 / 7
7h = 5 (h + r )
7h = 5h + 5r
7h – 5h = 5r
2h = 5r
h / r = 5 / 2
h : r = 5 : 2
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Q.5) 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 = h = 20cm
Diameter = 21cm
Radius = 21 / 2cm
Area of cardboard required = ?
Area of cardboard required = CSA + 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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