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How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m

A.

5600

B.

600

C.

6400

D.

7200

Answer with explanation

Answer: Option CExplanation

No. of bricks= volume of the wall/volume of 1 brick

= (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400

Workspace

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:

A.

20 cm

B.

25 cm

C.

35 cm

D.

50 cm

Answer with explanation

Answer: Option BExplanation

Workspace

The length, width, and height of a room are 7 m, 8 m, and 9 m respectively. What is the total area of the walls?

A.

270 sq. m.

B.

260 sq. m.

C.

265 sq. m.

D.

255 sq. m.

Answer with explanation

Answer: Option AExplanation

Area of the 4 walls of a room = 2 (Length + Breadth) * Height

Given that, Length = 7 meters, Width or Breadth = 8 meters and Height = 9 meters

So, the required area, A = 2 (7 + 8) * 9

= 2 * 15 * 9

= 270 sq. m.

Workspace

What is the area of the largest circle that can be drawn inside a square of side 20 cm?

A.

90 π cm^{2}

B.

100 π cm^{2}

C.

110 π cm^{2}

D.

95 π cm^{2}

Answer with explanation

Answer: Option BExplanation

The diameter of the largest circle that can be drawn inside a square = length of the side of the square

As per the question: The side of the square = 20 cm.

So, radius of the circle = 20/2 = 10 cm

Area of a circle = π × radius^{2}

The area of the largest circle = π × 102 = 100 π cm^{2}

Workspace

The difference between the length and breadth of a rectangle is 25 meters. If the perimeter of this rectangle is 210 meters, what is its area?

A.

3600 m^{2}

B.

2600 m^{2}

C.

3000 m^{2}

D.

2000 m^{2}

Answer with explanation

Answer: Option BExplanation

The perimeter: 2 (L + B) = 210 or L+ B = 105 …… (i)

As per the question: (L – B) = 25 ……. (ii)

Solving the above two equations:

L + B = 105

B = 105 – L

Put the value of B in (ii).

L – (105 – L) = 25

L – 105 + L = 25

2L = 25 + 105

2L = 130

L = 65

So, – B = 105 – 65 = 40

Now, area of a rectangle: L *B= 65 * 40 = 2600 m^{2}

Workspace

The height of a room to its semi-perimeter is 2: 5. It costs Rs. 260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per meter allowing an area of 15 cm^{2} for doors and windows. The height of the room is

A.

2.6 m

B.

3.9 m

C.

4 m

D.

4.2 m

Answer with explanation

Answer: Option CExplanation

Workspace

The sides of a rhombus are 10 cm in length, and one diagonal is 16 cm. The area of the rhombus is

A.

96 cm^{2}

B.

95 cm^{2}

C.

94 cm^{2}

D.

93 cm

Answer with explanation

Answer: Option AExplanation

When d_{1} and d_{2} are the diagonals of rhombus then,

The Side of rhombus =

Squaring both sides

20^{2} = 16^{2} + d_{2}^{2}

400 = 256 + d_{2}^{2}

d_{2}^{2} = 400 – 256

d_{2} = √144

d_{2} = 12

Area of rhombus =1/2( d_{1} × d_{2} )

=1/2 ( 16 × 12 )=96 cm^{2}

Workspace

A rectangular grass field has a length of 85 meters and breadth of 65 meters. It is surrounded by a 5-meter wide path. Find the area of the Path and the cost of constructing it at Rs. 5 per square meter?

A.

4000

B.

6000

C.

8000

D.

7000

Answer with explanation

Answer: Option CExplanation

Area of the entire grass field including the path = Length (85 + 5 +5) * Breadth (65 + 5+5)

= 95 * 75 = 7125 sq. m.

Area of the grass field excluding the path = 85 * 65 = 5525 sq. m.

So, area of the path = 7125 – 5525 = 1600 sq. m.

The cost of constructing is Rs. 5 per square meter.

So, the cost of constructing the entire path = 1600 * 5 = Rs. 8000

Workspace

The perimeter of the rectangular field is 480 meters and the ratio between the length and breadth is 5:3. Find the area of the field.

A.

7200 m^{2}

B.

15000 m^{2}

C.

13500 m^{2}

D.

54000 m^{2}

Answer with explanation

Answer: Option CExplanation

Let the length of the rectangle be 5x, and breadth be 3x,

Perimeter of a rectangle = 2(l +b) = 480

2(5x + 3x) = 480

2 x 8x = 480

16x = 480

x = 480/16 = 30

∴ Length = 5 x 30 = 150 m

Breadth = 3 x 30 = 90 m

And, Area of rectangle = L x B

= 150 x 90 = 13500 m^{2}

Workspace

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