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Quantitative Aptitude

VOLUME AND SURFACE AREA MCQs

Total Questions : 820 | Page 8 of 82 pages
Question 71.

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

  1.    4830
  2.    5120
  3.    6420
  4.    8960
 Discuss Question
Answer: Option B. -> 5120

Clearly, l = (48 - 16)m = 32 m,


b = (36 -16)m = 20 m,


h = 8 m.


So,  Volume of the box = (32 x 20 x 8) m3 = 5120 m3

Question 72.

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

  1.    3 : 7
  2.    7 : 3
  3.    6 : 7
  4.    7 : 6
 Discuss Question
Answer: Option B. -> 7 : 3

\(\frac{\pi r^{2}h}{2\pi rh} = \frac{924}{264}\Rightarrow r= \left(\frac{924}{264}\times2\right) = 7m\)


And, \(2\pi rh\Rightarrow h= \left(264\times\frac{7}{22}\times\frac{1}{2}\times\frac{1}{7}\right) = 6m.\)  


So, Required ratio =  \(\frac{2r}{h}=\frac{14}{6}= 7:3.\)

Question 73.

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

  1.    90 cm
  2.    1 dm
  3.    1 m
  4.    1.1 cm
 Discuss Question
Answer: Option B. -> 1 dm

Let the thickness of the bottom be x cm.


Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000


 320 x 250 x (110 - x) = 8000 x 1000


(110 - x) = \(\frac{8000\times1000}{320\times250}=100\)


x = 10 cm = 1 dm.

Question 74.

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

  1.    344.35 cm2
  2.    462 cm2
  3.    498.35 cm2
  4.    None of these
 Discuss Question
Answer: Option C. -> 498.35 cm2

h = 14 cm, r = 7 cm.


So, l = (7)2 + (14)2 = 245 = 75 cm.


So, Total surface area = \(\pi rl+\pi r^{2}\)


= \(\left(\frac{22}{7}\times7\times75+\frac{22}{7}\times7\times7\right)cm^{2}\)


= [154(5 + 1)] cm2


= (154 x 3.236) cm2


= 498.35 cm2.

Question 75.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

  1.    2 : 1
  2.    3 : 2
  3.    25 : 18
  4.    27 : 20
 Discuss Question
Answer: Option C. -> 25 : 18

Volume of the large cube = (33 + 43 + 53) = 216 cm3.


Let the edge of the large cube be a.


Let the edge of the large cube be a.


So, a3 = 216     \(\Rightarrow\)      a = 6 cm.


So, Required ratio =  \(\left(\frac{6\times(3^{2}\times4^{2}\times5^{2})}{6\times6^{2}}\right)=\frac{50}{36}= 25:18.\)

Question 76.

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

  1.    5600
  2.    6000
  3.    6400
  4.    7200
 Discuss Question
Answer: Option C. -> 6400

Number of bricks = \(\frac{Volume of the wall}{Volume of 1brick}=\left(\frac{800\times600\times22.5}{25\times11.25\times6}\right)= 6400.\)

Question 77.

A rectangular tank can hold 650 litres of milk . if it is 130cm long & 250cm wide , find the height of the tank?

  1.    10 cm
  2.    20 cm
  3.    30 cm
  4.    40 cm
  5.    None of these
 Discuss Question
Answer: Option B. -> 20 cm
 -    Volume of rectangular tank = 650 litres = 650 × 1000 cm 3 = 650000 cm 3
  We know that Volume of a cuboid = l × b × h
  650000 = 130 × 250 × h
  ⇒ h = (650000)/( 130 × 250 )= 20 cm
  Therefore, height of the tank = 20 cm
Question 78.

A hall is of length 16m , breadth 14m & height 5m . Calculate the no of persons that can be accommodated in the hall , assuming 3.5m3 of air is required for each person?

  1.    240 men
  2.    280 men
  3.    320 men
  4.    360 men
  5.    None of these
 Discuss Question
Answer: Option C. -> 320 men
 -  ∴Volume of the hall = length × breadth × height
                                                  = 16 × 14 × 5
                                                  = 1120 m3
  Volume occupied my 1 man = 3.5 m3
  3.5 m3  of air occupied my 1 man
  1120 m3  of air occupied my ( 1/3.5)x 1120= 320 man
  Therefore, number of men that can be accommodated = 320men
Question 79.

A cylinder container with diameter 48cm contains sufficient water to submerge a rectangular solid of iron with dimensions 33cm x 18cm x 12cm. Find the rise in the level of water when solid is completely submerged?

  1.    2.94 cm
  2.    3.94 cm
  3.    4.94 cm
  4.    5.94 cm
  5.    None of these
 Discuss Question
Answer: Option B. -> 3.94 cm

 -    Diameter of cylinder = 48 cm     
  ⇒ Radius of cylinder (r) = 24 cm
  Now, when the Cuboid  is completely submerged
  Then, Volume of cylindrical portion formed by original water level and after increase in water level =
   volume of cuboid
  ⇒ πr 2 h = 33 cm × 18 cm × 12 cm
  22/7 x 24 x 24 x h = 33 cm × 18 cm × 12 cm
  h = (33 cm × 18 cm × 12 cm x7)/ 22 x 24 x 24=3.94cm
  Hence, the required increase in water level is 3.94 cm


We are given a cylinder container with diameter 48cm which contains sufficient water to submerge a rectangular solid of iron with dimensions 33cm x 18cm x 12cm. We need to find the rise in the level of water when the solid is completely submerged.

Let's first find the volume of the rectangular solid of iron:

Volume of the rectangular solid = Length x Breadth x Height

= 33cm x 18cm x 12cm

= 7128 cubic cm

Now, let's find the volume of water displaced when the solid is completely submerged in the cylinder container. Since the volume of water displaced will be equal to the volume of the solid, we have:

Volume of water displaced = 7128 cubic cm

Let's find the height by which the level of water will rise in the cylinder container:

Volume of water displaced = πr^2h

where r is the radius of the cylinder and h is the height by which the level of water will rise.

Since the diameter of the cylinder is given as 48cm, the radius will be half of it, i.e., r = 24cm.

Substituting the values in the formula above, we get:

7128 = π x 24^2 x h

h = 7128 / (π x 24^2)

h ≈ 3.94 cm

Therefore, the rise in the level of water when the solid is completely submerged is 3.94 cm.

Hence, the correct option is B. 3.94 cm.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 80.

The difference between the circumference and radius of a circle is 74 cm. Find the circle diameter?

  1.    16 cm
  2.    24 cm
  3.    28 cm
  4.    32 cm
  5.    None of these
 Discuss Question
Answer: Option C. -> 28 cm
 -  circumference - radius = 74 
      pie d- d/2 =74 
    22d/7  - d/2 =74
   (44d-7d)/14 =74 
   37d = 74x14 
   d= (74x14)/37 
   d  = 28cm

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