aptitude : : volume and surface
 
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   Exercise 2
   Exercise 1
1.
A cone and a sphere have the same radius and the same volume. The ratio of the diameter of the sphere to the height of the cone is
 
A.
1 : 3

B.

3 : 2
C.
1 : 2
D.
2 : 3
   
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Answer: C
Explanation :

Suppose the radius and height of the cone are r an h respectively.

Radius of the sphere = r

According to question :

Volume of the cone =  Volume of the sphere

(1/3) πr2h  = (4/3) πr3  => h = 4r

Diameter : Height  = 2r : h = 2r : 4r  [h=4r]

                                               = 1 : 2







 
2.
Two cylindrical jars have their diameters in the ratio 3 : 1. If their height are in the ratio 2 : 1, then the ratio of their volumes will be
 
A.
18 : 1

B.

14 : 3
C.
3 : 5
D.
1 : 18
   
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Answer: A
Explanation :

Suppose diameter of the two cylinder jars are 6X and 2X.

Their radio will be 6X/2 = 3X  and 2X/2 = X

While their height are 2H and H respectively

Hence their volums will be π(3X)2*2H and π*(X)2*H respectively

Ratio of their volumes

                                                = π*9x2*2H : πr2H  = 18 : 1







 
3.
The surface area of a cylinder is 528 sq. cm while its height is 8 cm. The volume of this cylinder will be
 
A.
2882 cu cm

B.

2772 cu cm
C.
3772 cu cm
D.
2782 cu cm
   
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Answer: B
Explanation :
Surface area of the cylinder = 2πrh
                                   2πrh   = 528
                                             r = 528/2πrh = (528*7)/(2*22*8) = 10.5 cm
Volume of the cylinder
                                = πr2h =  (22/7)*(10.5)2*8  = 2772 cu cm.






 
4.
If the volumes of two cubes are in the ratio 27 : 1 the ratio of their edges is
 
A.
1 : 3

B.

1 : 27
C.
3 : 1
D.
27 : 1
   
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Answer: C
Explanation :
Let their edges be A and  B
                A3/B3  =  (27/1)(A/B)3  = (3/1)3
                A : B    =   3 : 1






 
5.
A wall 8.0 m long, 3.6 m high and 0.8 m thick is to be constructed with bricks each 20 cm * 12 cm * 5.6 cm. If the motar used increases the volume of each brick by (1/7) of its original volume, find the number of bricks required to construct the wall
 
A.
15000

B.

17000
C.
14000
D.
13000
   
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Answer: A
Explanation :
Volume of the wall
      = 8*3.6*0.8  = 23.04 cu m or 23040000cu cm
Volume of the brick = 20*12*5.6 = 1344 cu cm
According to question:
Volume of a brick including the motar
                                = 1344 +(1/7) of 1344
                                = 1344 + 192 = 1536 cu cm

Number of bricks required

                                = (volume of the wall/volume of a brick including motar)

                                =23040000/1536

                                = 15000







 
6.
If the radius of a sphere is decreased by 50%, then by how much percent will the surface area of this sphere by decreased?
 
A.
50%

B.

40%
C.
60%
D.
75%
   
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Answer: D
Explanation :

Surface area of the sphere comprises two edges ( i.e., radius * radius)

Percentage decrease in each of the first and the second edge will be 50%, i.e., X% = Y% = 50%

And in case of the percentage decrease values of X and Y will be negative.

Change in surface area of the sphere

              ((-50)-50+((-50)*(-50))/100)%  = (-100+25)%  = -75%

Hence surface area of the sphere will be decreased by 75%







 
7.
If the whole mass of a sphere can be tightly placed in a cube, then the volume of the cube and the volume of the sphere are in the ratio
 
A.
7 : 12

B.

22 : 21
C.
21 : 11
D.
20 : 7
   
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Answer: C
Explanation :
The sphere can be completely fitted in the cube. It means side of the cube is equal to the diameter of the sphere.

Radius of the sphere  = (Diameter)/2

Volume of the sphere     = (4/3)π(r)3

And volume of the cube = (side)3
Ratio of the volumes of the cube and the sphere
                                                = (side)3 : (4/3)πr3
                                              =>(diameter)3  : (4/3)π(r)3
                                                =>         (2*r)3  : (4/3)π(r)3
                                                                       2 : (1/3)π  
                                                                       6 : π = 6 : (22/7)  = 42 : 22 = 21 : 11






 
8.
A cube of edge 5 cm is cut into cubes each of edge 1 cm the ratio of the total surface area of one of the small cubes to that of that of the large cube is equal to
 
A.
1 : 5

B.

1 : 25
C.
1 : 125
D.
1 : 625
   
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Answer: B
Explanation :
Required ratio = ((6*1*1)/(6*5*5)) = 1/25  = 1 : 25






 
9.
An iron cube of side 10cm is hammered into a restangukar sheet of thickness 0.5cm. 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
   
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Answer: B
Explanation :

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

                          5X2  = 2000

                            X2  = 400

                             X  = 20

The sides are 20 cm and 100 cm







 
10.
A cuboidal block of 6cm*9cm*12m is cut up into an exact number of equal cubes.The least possible of cubes will be
 
A.
6

B.

9
C.
24
D.
30
   
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Answer: C
Explanation :
Volume of block        =  6*9*12 = 648 cm3
Side of largest cube =  4 CF of 6, 9, 12 = 3 cm
Colume of this cube = 3*3*3 = 27 cm3
 
Number of cubes       = 648/27  = 24






 

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