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MENSURATION

1. The area of a rectangular plate is 231.25 sq.cm. If the length of the plate is 18.5 cm, find the perimeter of the plate.
Sol: Width of the field   
Perimeter = 2(length + width)
                   2 (18.5 + 12.5) = 62 cm


2. How many tiles of 20 cm length and 10 cm width are required to pave the floor of a room 8 m long and 5 m wide?
Sol: Area of the floor of the room = 800 × 500
                            = 400000 cm2
Area of theTile = 20 × 10 cm2
Number of Tiles required  


3. A square field has an area of 50625 sq. m. Find the cost of fencing around it at Rs.15 per meter.
Sol: Side of the square field = 
Length of the wire required = 4 × 225 = 900 m
Total cost = Rs.15 × 900 = Rs.13500


4. A horse is tied with a 14 m long rope. How much ground will it be able to graze?
Sol: Length of the rope will be the radius of the
circle = 14 m
Area of the cicrle = π r2 
   
... Area of the ground that can be grazed = 616 sq.m

 

5. Find the length of the longest stick that can be placed in a room of 12 m long, 9 m broad and 8 m high.
Sol: Length of the stick = length of the diagonal of the room


6. A rectangular field of 60 meter length and 40 meters wide is to be surrounded by a road 5 meter wide. If the cost of making 1 square meter road is Rs.500, what would be the cost of the entire road?
Sol: Area of the road = Area of outside rectangle − Area of inside rectangle
                                     = 70 × 50 − 60 × 40
                                     = 3500 − 2400 = 1100 m2
... The cost of making 1100 m2 = 500 × 1100
                                 = Rs.550000


7. What will be the area of a triangle with base 10.2 cm and height 3.5 cm?
Sol: Area of triangle
 
  

8. The breadth of a rectangular plot is 75% of its length. If the perimeter of the plot be 1050 m, what is its area?
A:  67500
EXPLANATION:
Let the length of the plot be x m


9. A room is 7.5 m long, 5.5 m broad and 5 m high. What will be the expenditure in covering the walls by paper 40 cm broad at the rate of 75 paise per meter?
A:  Rs.243.75
EXPLANATION:
Area of four walls = 2 × 5 (7.5 + 5.5)
                                = 130 m2
Area of required paper = 130 m2
Breadth of the paper = 40 cm
                           = 0.4 m

... Cost of paper at 75 paise per meter  = 325 × 0.75                                                                   
                             = Rs.243.75


10. Two cubes have their volumes in the ratio 8 : 27. Find the ratio of their surface areas.
A:  4 : 9
EXPLANATION:
a13 : a23 = 8 : 27  a1: a2 = 2 : 3
... Surface areas ratio = 6a12 : 6a22  = (2)2 : (3)2 = 4 : 9


11. The length and breadth of a rectangle increased by 20% and 10% respectively. How much percent will its area be increased?
A:  32%
EXPLANATION:
Let the length and breadth be10 and 10
Area = 10 × 10 =100
New length = 12 (20% increase)
New breadth = 11(10% increase)
New area = 12 × 11= 132
... Increment in area =132 − 100 = 32%    


12. 7 cm radius and 28 cm height solid metallic cylinder is melted and recast into small spherical balls of 7 cm radius. Find the number of cubes that can be made.
A:  3
EXPLANATION:
Let the number of spherical balls be 'x'
Volume of cylinder = x × Volume of sphere

Posted Date : 10-02-2021

 

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