aptitude : : volume and surface

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 Overview Important Formulas Exercise 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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%

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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

Answer Discuss in Forum Calculator Workspace
 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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