Lakshya Education MCQs

Question:

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Options:
A.84
B.90
C.168
D.336
Answer: Option A

Let the length of the wire be h.

Radius = \(\frac{1}{2}mm=\frac{1}{20}cm. Then,\)

\(\frac{22}{7}\times\frac{1}{20}\times\frac{1}{20}\times h= 66 \) 

h =  \(\left(\frac{66\times20\times20\times7}{22}\right)=8400cm=84 m.\)

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More Questions on This Topic :

Question 1.

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

Options:
  1.    720
  2.    900
  3.    1200
  4.    1800
Answer: Option C

2(15 + 12) x h = 2(15 x 12)

h =  \(\frac{180}{27}m=\frac{20}{3}m.\)

So, volume =  \(\left(15\times12\times\frac{20}{3}\right)m^{3} = 1200m^{3}\)

Question 2.

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Options:
  1.    75 cu. m
  2.    750 cu. m
  3.    7500 cu. m
  4.    75000 cu. m
Answer: Option B

1 hectare = 10,000 m2

So, Area = (1.5 x 10000) m2 = 15000 m2.

Depth = \(\frac{5}{100}m = \frac{1}{20}m\) 

So, Volume = (Area x Depth) =  \(\left(15000\times\frac{1}{20}\right)m^{3}=750m^{3.}\)

Question 3.

 A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

Options:
  1.      \(12\pi\) cm3
  2.       \(15\pi\)cm3
  3.      \(16\pi\) cm3
  4.      \(20\pi\) cm3
Answer: Option A

Clearly, we have r = 3 cm and h = 4 cm

So \(Volume,= \frac{1}{3}\pi r^{2}h = \left(\frac{1}{3}\times \pi\times3^{2}\times4\right)cm^{3} =12\pi cm^{3}.\)

Question 4.

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

Options:
  1.    3.6 kg
  2.    3.696 kg
  3.    36 kg
  4.    36.9 kg
Answer: Option B

External radius = 4 cm,

Internal radius = 3 cm.

Volume of iron  =  \(\left(\frac{22}{7}\times\left[(4)^{2}-(3)^{2}\right]\times21 \right)cm^{3}\)

= \(\left(\frac{22}{7}\times7\times1\times21\right)cm^{3}\)

=  462 cm3.

So, Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.

Question 5.

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

Options:
  1.    12 kg
  2.    60 kg
  3.    72 kg
  4.    96 kg
Answer: Option B

Volume of water displaced = (3 x 2 x 0.01) m3

= (0.06 x 1000) kg

= 60 kg.

Question 6.

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 m3, then the rise in the water level in the tank will be:

Options:
  1.    20 cm
  2.    25 cm
  3.    35 cm
  4.    50 cm
Answer: Option B

Total volume of water displaced = (4 x 50) m3 = 200 m3.

So, Rise in water level = \(\left(\frac{200}{40\times20}\right)m0.25m=25cm.\)