Area and Volume


Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.

1. Find the volume of a cube whose perimeter of each face is 20 feet.

A. 125

B. 64

C. 216

D. 81


                  Ans: Option A


       The perimeter of one face of a cube = 20 feet

       The face of a cube has 4 edges.

       The length of an edge of the cube = 20/4 = 5 feet.

       The volume of the cube having A as an edge is A3 unit3.

       Then volume = 53 = 125 feet3.

       Hence the answer is 125. 

2. The length of diagonal of a cube is (14 x) cm. The volume of the cube is:

 A. 2748 cm3

 B. 2744 cm3

 C. 588 cm3

 D. 3528 cm3


                  Ans: Option B


       No explanation 

3. The maximum length of a pencil that can be kept in a rectangular box of dimension 8 cm x 6 cm x 2 cm, is :

A. 2 cm

B. 5 cm

C. 8 cm

D. 10 cm


                  Ans: Option A


       No explanation 

4. Find the total surface area of the cube whose volume is 1000cm3.

A. 600 cm2

B. 100 cm2

C. 200 cm2

D. 586 cm2


                  Ans: Option A


       The volume of a cube having side a = a3.

       Given a3 = 1000

       Then a = 10 cm

       Total surface area = 6a2cm2

       = 6 x (10)2 = 6 x 100 = 600cm2.

       Hence the answer is 600cm2. 

5. A river 2 m deep and 45 m wide is running at the rate of 3 km/hr. The amount of water that runs into the sea per minute, is:

A. 4500 m3

B. 27000 m3

C. 3000 m3

D. 2700 m3


                  Ans: Option A


       No explanation 

6. 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


                  Ans: Option C


       2(15 + 12) x h = 2(15 x 12)

       h = 180/27 m = 20/3 m.

       Volume = (15 x 12 x 20/3)m3 = 1200 m3. 

7. 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 m3. The breadth of the wall is:

A. 30 cm

B. 40 cm

C. 22.5 cm

D. 25 cm


                  Ans: Option B


       No explanation 

8. 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:

A. 12 π cm3

B. 15 πcm3

C. 16 π cm3

D. 20 π cm3


                  Ans: Option A


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

       Volume = 1/3 x π x r2 x h

                    =  (1/3 x π x 32 x 4 )cm3

                    = 12  cm3. 

9. The area of the base of a rectangular tank is 6500 sq. cm. and the volume of water contained in it 2.6 cubic meters. The depth of water is :

A. 3.5 m

B. 4 m

C. 5 m

D. 8 m


                  Ans: Option B


       No explanation 

10. A cylinder of radius 5m and height 7m is melted to form 11 equal cuboids. Find the volume of the cuboid.

A. 10 m³

B. 20 m³

C. 50 m³

D. 100 m³


                  Ans: Option C


       Volume of the cylinder =pir²h = 550m³

       Volume of the cuboid

       = volume of the cylinder/no of cuboid formed

       = 550/11 = 50 m³ 

11. If each side of a cube is doubled, then its volume :

A. is doubled

B. becomes 4 times

C. becomes 6 times

D. becomes 8 times


                  Ans: Option D


       No explanation 

12. The number of revolutions a wheel of diameter 21cm takes in travelling a distance of 396m is

A. 600m

B. 300m

C. 150m

D. 115m


                  Ans: Option A


       Diameter(d)=21cm, Distance=396m=39600cm

       No. of revolutions = Distance travelled/Circumference

       = 39600/ π*d = 600 

13. The area of the largest square that can be inscribed in a circle of radius 5cm is

A. 12.5 cm²

B. 25 cm²

C. 50 cm²

D. 100 cm²


                  Ans: Option C



       So, side of the square is 5cm,Therefore

       Diagonal of the square = Diameter of the circle

2a = 2r = 10cm

a²=50 cm²

14. The area of the largest circle that can be inscribed in a square of side a is

A. ?a²/4

B. ?a²/2

C. ?a²/8

D. ?a²


                  Ans: Option A


       Let, the radius of the circle is r

       Diameter of the Circle=Side of the square=2r=a

       Area = pia²/4 

15. A 3 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

A. 3:1

B. 1:3

C. 1:9

D. 27:1


                  Ans: Option B


       Surface area of a 3 cm cube =6*3² = 54 cm²,

       Surface area of a 1 cm cube =6*1² = 6 cm²

       No. of smaller cubes formed = Volume of larger cube/Volume of smaller cube

       =3³/1³ = 27 Ratio = 54/(27*6) = 1(cat) 

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