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### Course Content  ### Mensuration

When a metallic ball bearing is placed inside a cylindrical container of radius 2cm, the height of the water inside the container increases by 0.6 cm. The radius to the nearest length of a centimeter of the ball bearing is 

1 cm

1.2 cm

2 cm

0.6 cm

A homeowner is planning to use carpet tiles to cover the floor of a room measuring 9 feet by 10 feet 8 inches. If the carpet tiles are 8 inches wide and 1 foot long and there are no gaps between the tiles as they are placed on the floor, how many carpets tiles will the home owner need to cover the floor of the room? 

100

135

144

150

The length of rectangular window is 5 feet more than its width. The area of the windows is 36 square feet. Which equation could be used to find the dimension of the window? 

w(w + 5) = 36

w + w + 5 = 36

w(w - 5) = 36

2w + 10 = 36

In a garden there are 10 rows and 12 columns of mango trees. The distance between the two tree is 12 meters and a distance of one of the meter is left from all of the boundary of the garden. The length of the garden is: 

20 m

22 m

24 m

26 m

A shop sells floor tiles at Rs 48 per square meter. A building contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the halls is of square shape has a perimeter of 400 meters? 

Rs 400,000

Rs 500,000

Rs 528,000

Rs 365,000

6. In a 400 meter race around a circular stadium having a circumference of 100m, the fast runner and slowest time after the same point at the end of the 5th minute, for the fast time after the race all the runners have the same starting point and each runner maintains a uniform speed of slowest runner, what is the time taken by the fastest runner to finish the race. 

20 minutes

15 minutes

10 minutes

5 minutes

What is the % change in the area of a square (which will become rectangle) If its length side is increased by 10% and its width side is decreased by 10%. In these type of problem, assume a percentage base and then move forward

5%

3%

2%

1%

What is the area of right triangle to the right? 

6

7

8

10

If (d) denotes the area of a circle with diameter d, then which of the following is equal to (4) x (6)? 

π(24)

π(12)

24

12

Length and breadth of a rectangular field is 50 meter and 20 meter respectively. A 7 meters wide road runs outside around the field. What is the area of the road? 

40 Sq m

1000 Sq m

1176 Sq m

1208 Sq m

If the length of rectangle is increased, by 20% and the width of the same rectangle decreased 

Decreased by 20%

Decreased by 4%

Increased by 20%

Increased by 4%

Solutions

New Length = 120l / 100
New Breadth = 90b / 100
New Area = 120l x 90b/10000
which is 108A/100
The area is increase by 8%

What is the ratio of the areas of a square and the square drawn on its diagonal? 

1 : 1

1 : 2

1: 3

1 : 4

Solutions

Let the side of square be a unit.
Area of this square = a2
The diagonal of square = √2a
∴ Area of square = 2a2
∴ Required Ratio = a2 : 2a2
= 1 : 2

The ice compartment of a refrigerator is 8 inches long, 4 inches wide and 5 inches high. How many ice cube will it hold if each cube is 2 inches on an edge? 

8

10

12

16

Solutions

The perimeter of a rectangular field is 320 meter and ratio of the length and breadth of the field is 5:3. What is the area of the rectangular field 

6000 meters square

650 meters square

5300 meter square

3200 meter square

Solutions

Length : Breadth = 5x : 3x
The perimeter is 320 m
Perimeter = 2(Length + Breath)
320 = 2 (5x + 3x)
320 = 2( 8x )
16x = 320
x = 20
5 x 20 = 100m
3 x 20 = 60m
area = l x b = 6000m

If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is:

15.12

13.52

12.62 sq cm

10.00 sq cm

Solutions

Side of square = Diagonal / √ 2
Area = Diagonal 2 / 2
27.04 / 2
13.52 I there is