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# Volume and Surface Area Questions

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Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,

A5.5 cm.

B4.5 cm.

C7.5 cm.

D6.5 c.m.

Explanation:

volume=l*b*h=6*5*2=60cm^3
now volume is reduced by 19%.therefore 81/100 *60=48.6
now,thickness remains same and let length and breadth be reduced by x%
so,new volume: 2*x/100 *6*x/100 *5=48.6
=>x=90 thus length and width is reduced by 90%
new width =90% of 5 =4.5

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A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?

A5 cms

B2 cms

C3 cms

D4 cms

Explanation:

The volume of the cylinder is Pi x r^2 x h = Pi x 3^2 x 6 = 54Pi
Volume of a cylinder is 4/3 x Pi x r^3
Now 54Pi = 12 x 4/3 x Pi x r^3
54 = 16 x r^3
r^3 = 54/16 = 27/8
r = 3/2
Therefore diameter is 3 cms

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Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?

A114

B135

C21

D71

Explanation:

((3*9*5))-((3-2)*(9-2)*(5-2))

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The radius of a sphere is increased by 50%. The increase in surface area of the sphere is :

A100%

B125%

C150%

D200%

Explanation:

Take here radius as 100.
So, surface area = 4*22/7*100*100. (Surface area of sphere = 4*pi*r^2)
As per condition:
After increase radius by 50% the new radius = 100+50% of 100=150,
So, new surface area = 4*22/7*150*150
Increase in surface area = ((4*22/7)*150*150 -(4*22/7)*100*100)/(4*22/7-100*100)=125%

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A polygon has 44 diagonals. Number of sides=?

A7

B11

C8

D9

Explanation:

No. of diagonals=[n(n-3)]/2
n=no. of sides
=> 44=(n2-3n)/2
=> n2-3n-88=0
=> n2-11n+8n-88=0
=> n=11

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A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immeresed. The water level in the vessel will rise by

A9/2 cm

B9/4 cm

C4/9 cm

D2/9 cm

ENone of these

Explanation:

volume of solid sphere = (4/3)*(22/7)*3*3*3

volume of cylindrical vessel = (22/7)*4*4*h

on equating both we get h = 9/4 cm

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A company decided to install a fountain within it main entrance lobby. If fountain is to be 148 cm wide 297 long and 91 cm deep. How much water would be required to feel the fountain to a depth of 69 cm?(1 liter=1000 cubic centimeters)

A4000

B5140

C3033

D5360

Explanation:

water filled will turn into depth. i.e. depth =69 cm
volume of water to fill the tank is = l*b*h
= 148*297*69=3032964 cubic cm.
1 cc= 1000 cu.cm
Therfore volume = 3032964/1000
=> volume = 3032.964 lts.

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A circular cylinder of internal diameter 8 cm and height 10 cm contain water to a depth of 6 cm.Two solid lead sphere each of diameter 4 cm are placed in it. Find height by which water level rises.

A2 cm

B10 cm

C1 cm

D1 1/3

Explanation:

Volume of cylinder = (pi*r^2*h)
column of sphere = ( (4*pi*r^3)/3)
r(sphere) = 2,
so volume of 2 sphere = 64pi/3.
r(cylinder) = 4,
pi * 4^2 * h = 64*pi/3
so, h = 4/3 = 1 1/3

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A spherical solid ball of radius 58 mm is to be divided into eight equal parts by cutting it four times longitudinally along the same axis.Find the surface area of each of the final pieces thus obtained( in mm^2) ? (where pi= 22/7)

A3365pi

B5046pi

C1682pi

D3346pi

Explanation:

If a sphere is cut into 8 parts longitudinally, It something looks like below Now We have to find the surface area of one piece. This is 1/8th of the initial sphere + 2 × area of the half circle
= 1/8(4?r^2)+?r2
= 1/8(4 * ? * (58)^2) + ? *(58)^2
= 5046pi

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A boy wants to make cuboids of dimension 5m,6m & 7m from small cubes of .03m^3.Later he realized that he can make some cuboids by making it hollow.
Then it takes some cubes less. What is the number of cubes to be removed

A2000

B5000

C3000

D7000

Explanation:

Total no of cubes = 5*6*7/0.03=7000
for making it hollow we have to remove (5-2)*(6-2)*(7-2)/0.03=2000.

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