Advanced Quiz Quiz For SSC

1.The diameter of the base of a cylinder is 14 cm and its height is 12 cm. What is the volume of the cylinder? 

(a) 1600 cm^3

(b) 1200 cm^3 

(c) 1848 cm^3 

(d) 2400 cm^3

2.The volume of a right circular cone is  196π cm^3 . If the area of its base is 154cm^2, what ithe vertical height of the cone? 

(a) 10 cm  

(b) 12 cm 
(c) 14 cm 
(d)  16 cm

3. A metallic sphere of radius  12 cm is melted and recasted into a cylinder, whose radius is 16 cm. What is the height of the cylinder?

(a) 9 cm                      

(b) 18 cm                           

(c) 90 cm                            

(d)  180 cm

4. A hemispherical tank of inner radius 7 m is completely filled with water. A pipe attached at the bottom of the tank is opened and the water is made to  completely flow into a cylindrical tank of base radius 7 m. The height to which the water level in the cylindrical tank rises is .

(a) 2 2/3 m  

(b) 3 1/3 m  

(c) 4 2/3 m  

(d) 5 1/3 m

5 . A road roller is in the shape of cylinder. The radius of the cross section is 14 cm and the length is 1 meter. What is the area covered by the roller in making  200 revolutions? 

(a) 176 m^2 

(b) 228 m^2 

(c) 154 m^2 

(d) 126 m^2

6.The length, breadth and height of a cuboid are respectively 8m, 5m and 3m. This is melted and converted into four equal cubes. In this process 10% of material is lost. What is the edge of each cube? 

(a) 2m 

(b) 3m 

(c) 4m 

(d) 6m 

7.A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? 

(a) 10 

(b) 100 

(c) 1000 

(d) 10000

8.Two cubes of sides 8 cm each are kept adjacent to each other. What is the total surface area of the cuboid formed? 

(a) 765 cm^2 

(b) 840 cm^2 

(c) 1210 cm^2 

(d) 640 cm^2

9.When a cubical metallic piece of edge 3 cm is dropped in a cylindrical glass of water, the water column rises by 3 cm. What is the radius of the base of the glass? 

(a) 2/√π cm

(b) 3/√π cm 

(c) 6/√π cm 

(d) 9/√π cm

10.A rectangular sheet of metal is 28 cm by 13 cm. Equal squares of side 3 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. What is the volume of this box? 

(a) 231 cm^3 

(b) 1092 cm^3 

(c) 462 cm^3 

(d) 362 cm^3

Explanation....

1.(c) Volume of the cylinder = πr^2 h

22/7 * 7 * 7 * 12 = 1848 cm^3

2.(b) 1/3 π r^2 h = 196π

=> r^2h = 196 * 3 ………….. (1)

Area of the base = pr^2 = 154

=> r^2 = 49

=> r = 7cm

h = 196 * 3/49 = 12

3.(a) Volume of the wire (Cylinder) is equal to the volume of the sphere.

π(16)^2  ×  h = 4/3 π(12)^3

=> h = 9 cm

4.(c)Let’ h be the water level in the cylindrical tank

= 2/3π(7)^3 = P(7)^2 h

=>h =14/3 = 4 2/3 m

5.(a) The area covered by the road roller in one revolution is its curved surface area.

so Area covered in 200 revolutions

= 200 * 2πrh = 200 * 2 * 22/7 * 14/100 * 1 = 176 m^2

6.(b) Volume of cuboid = 8 * 5 * 3 = 120 cubic. m

Material lost = 10% of 120 =   12m^3.

so Remaining material = 120- 12 = 108m^3

Let a be the edge of the cube, then

4a^3 = 108 gives a = 3m

7. (c) Along one edge, the number of small cubes that can be cut = 100/10 = 10

Along each edge 10 cubes can be cut. (Along length, breadth and height).

Total number of small cubes that can be cut = 10 * 10 * 10 = 1000

8.(d) The length of the cuboid formed will be 16 cm, its breadth and height remains 8 cm each.

Total surface area = 2lb + 2bh + 2hl

= 2(16)(8) + 2(8)(8) + 2(8)(16)

= 640 cm^2

9.(b) Volume of the cubical metallic piece

= volume of the water column

= 3 * 3 * 3 = p (r^2) (3)

= π (r^2)(3)= 3 * 3 * 3

=3/√π cm

10.(c) When 3 cm * 3 cm squared are cut off at corners,

the rectangular box has dimensions of 28 – 6 = 22 cm length,

13 – 6 = 7 cm breadth and 3 cm height

so Volume = 22 * 7 * 3 = 462 cm^3