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Q:

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

A) 8.04kg	B) 8.14kg
C) 8.24kg	D) 9.04kg

Answer & Explanation Answer: A) 8.04kg

Explanation:

Volume of the metal used in the box = External Volume - Internal Volume

= [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm

= 16080 cu.cm

Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

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Filed Under: Volume and Surface Area

Q:

Water flows into a tank 200 m x 160 m through a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 meters?

A) 92min	B) 93min
C) 95min	D) 96min

Answer & Explanation Answer: D) 96min

Explanation:

Volume required in the tank = (200 x 150 x 2) cu.m = 60000 cu.m

Length of water column flown in1 min =(20 x 1000)/60 m =1000/3 m

Volume flown per minute = 1.5 x 1.25 x (1000/3) cu.m= 625 cu.m.

Required time = (60000/625)min = 96min

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Filed Under: Volume and Surface Area

Q:

Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?

A) 35000	B) 45000
C) 55000	D) 65000

Answer & Explanation Answer: B) 45000

Explanation:

Volume of the wall = (2400 x 800 x 60) cu.cm

Volume of bricks = 90% of the volume of the wall

= [(90/100) x 2400 x 800 x 60] cu.cm

Volume of 1 brick = (24 x 12 x 8) cu.cm

Number of bricks = [(90/100) x (2400 x 800 x 60) ]/ (24 x 12 x 8) = 45000

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Filed Under: Volume and Surface Area

Q:

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A) 40cm	B) 30cm
C) 20cm	D) 10cm

Answer & Explanation Answer: A) 40cm

Explanation:

Let the breadth of the wall be x metres.

Then, Height = 5x metres and Length = 40x metres.

x * 5x * 40x = 12.8

=> $x^{3} = 12.8 / 200 = 128 / 2000 = 64 / 1000$

=> x = 4/10 m

=> x = (4/10)*100 = 40 cm

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Filed Under: Volume and Surface Area

Q:

Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.

A) 14m	B) 15m
C) 16m	D) 17m

Answer & Explanation Answer: D) 17m

Explanation:

Length of longest pole = Length of the diagonal of the room

$[\sqrt{12^{2} + 8^{2} + 9^{2}}] = \sqrt{289} = 17 m$

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Filed Under: Volume and Surface Area

Q:

Find the surface area of a cuboid 16 m long, 14 m broad and 7 m high

A) 868 sq.cm	B) 920 sq.cm
C) 727 sq.cm	D) 900 sq.cm

Answer & Explanation Answer: A) 868 sq.cm

Explanation:

Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] sq.cm

= (2 x 434)sq.cm = 868 sq.cm

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Filed Under: Volume and Surface Area

Q:

I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?

A) 1/999	B) 1/1001
C) 1/1000	D) 4/1000

Answer & Explanation Answer: C) 1/1000

Explanation:

It is given that last three digits are randomly dialled. then each of the digit can be selected out of 10 digits in 10 ways.
Hence required probability = ${(\frac{1}{10})}^{3}$ = 1/1000

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Filed Under: Probability

Q:

What is the probability of getting at least one six in a single throw of three unbiased dice?

A) 1/36	B) 91/256
C) 13/256	D) 43/256

Answer & Explanation Answer: B) 91/256

Explanation:

Find the number of cases in which none of the digits show a '6'.

i.e. all three dice show a number other than '6', 5×5×5=125 cases.

Total possible outcomes when three dice are thrown = 216.

The number of outcomes in which at least one die shows a '6' = Total possible outcomes when three dice are thrown - Number of outcomes in which none of them show '6'.

=216−125=91

The required probability = 91/256

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Filed Under: Probability

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