Quant Quiz on Volume and Surface Area

Dear Readers,
We are providing you the  basics of the most important chapter i.e  ” Volumes and Surface Area”. Most of the students think that they are comfortable with these question but some times even a minor mistake can make a huge difference. So go through these formula and remember it in future.These questions will be helpful for SSC Exams.
1. Cuboid :
Let length = l, breadth = b and height = h units. Then
1. Volume = (l x b x h) cubic units.
2. Surface area = 2(lb + bh + lh) sq. units.
3. Diagonal = √l^2 + b^2 + h^2 units.



2. Cube :
Let each edge of a cube be of length a. Then,
1. Volume = a^3 cubic units

2. Surface area = 6a^2 sq. units.
3. Diagonal =√ 3a units.


Questions on Above Formula
1.A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to
A.1 : 5
B.1 : 25
C.1 : 125
D.1 : 625


2.The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is
A.8500 cm^3
B.9000 cm^3
C.9250 cm^3
D.9261 cm^3


3.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 man is
A.12 kg
B.60 kg
C.72 kg
D.96 kg


4.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?
A.5600
B.6000
C.6400
D.7200


5.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:
A.720
B.900
C.1200
D.1800


6.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:
A.3.6 kg
B.3.696 kg
C.36 kg
D.36.9 kg


7.A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is
A.12pie cm^3
B.15pie cm^3
C.16pie cm^3
D.20pie cm^3


8.The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is
A.3 cm
B.4 cm
C.6 cm
D.8 cm


9.Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be
A.125 cm^3
B.625 cm^3
C.15525cm^3
D.1225cm^3


10.An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
A.10 cm, 50 cm
B.20 cm, 100 cm
C.40 cm, 200 cm
D.None of these


Answer With Explanations:

1.(6x1x1 / 6x5x5)
‹=› 1/ 25
‹=› 1 : 25.

2.Surface area    = (34398 / 13)
‹=›2646cm^3
‹=›6a^2= 2646
‹=›a^2= 441
‹=›a = 21.
So,volume =(21x21x21)cm^3= 9261cm^3

3.Volume of water displaced    = (3 x 2 x 0.01)m^3
= 0.06m3.
Mass of man     =Volume of water displaced ×Density of water
= (0.06×1000) kg
= 60 kg.

4.Number of bricks = Volume of the wall/Volume of 1 brick
=(800x600x22.5 /25×11.25×6)
= 6400

5. 2(15 + 12) ×h = 2(15 x 12)
‹=›h= 180/27 m
= 20/3m
Volume    = (15×12×20/3)m^3
‹=›1200 m^3.

6. External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron    =(22/7×(42)-(32)×21)cm^3
= (22/7×7 ×1×21)cm^3
= 462 cm^3.

7.(a)

8. 4?R^2= 2?6×12
R^2 = (6×12/2)= 36
R = 6 cm.

9.The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm
Volume = (25x5x5)cm^3
‹=›625cm^3

10.Let the sides of the sheet be x and 5x.
Then,volume of the sheet= volume of the cube
‹=› x × 5x ×1/2
‹=› 10×10×10
‹=› 5x^2= 2000
‹=› x^2= 400
‹=› x = 20.
The sides are 20 cm and 100 cm.

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