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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 6 cm long 5cm wide and 2 cm thick. To cut costs the company had decided to reduced the volume of bar by 19%. The thickness will remain the same, but the length and width will be decreased by the same %. The new width will be


A6.5

B5.5

C7.5

D4.5

Answer: Option D

Explanation:

Volume = l*b*h
=> 6*5*2 = 60cm^3
Volume is reduced by 19%
New Volume = (100-19)100*60 = 486000 = 48.6
Thickness is same but length and breadth reduces by x%
So,new volume = (x/100*6)(x/100*5)2 = 48.6
=> x=90
So, Length and Breadth reduced by 10%
=> new width = 5-(10 * 5/100) = 4.5

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A conical tent is to accommodate 10 persons. Each person must have 6 sq.meter space to sit and 30 cubic meter of air to breathe. What will be the height of the cone?


A150m

B37.5 m

C15 m

D75 m

Answer: Option C

Explanation:

Amount of area reqd. by 1 person to stand = 6 sq.metre
Amount of area reqd. by 10 person to stand = 6x10 sq.metre i.e 60 sq.metre
So,
Base Area, pi*r*r=60
=>r*r = 60/pi ---------------(1)
Now,
Volume of air reqd. to breathe 1 person= 60 cu.metre
Volume of air reqd. by 10 person to breathe = 60x10=600 cu.metre
So,
Volume, 1/3*pi*r*r*h = 300 ---------------------(2)
Putting the value of eqn 1 in eqn 2, we get
1/3*pi*60/pi*h = 300
=> 1/3*60*h = 300
=> 20*h = 300
=> h = 300/20 = 15
Therefore height = 15 metres

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What is the volume of hemisphere of radius 5 cm?


A250/3 pi

B500/3 pi

C50/3 pi

D350/3 pi

Answer: Option C

Explanation:

Volume of a hemisphere= 2/3 *pi* r^3



2/3* pi* 5^3= 250 pi/3

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A solid iron cylinder of radius 4 cm and height 18 cm is melted and recast into a sphere. What is the radius of the sphere?


A4 cm

B6 cm

C18 cm

D9 cm

E12 cm

Answer: Option B

Explanation:

volume of cylinder = pi * r^2 * h
volume of sphere = 4/3 * pi * r^3
as cylinder is melted therefore volume of both will remain same therefore equating both we get
r^3=216
=> r = 6 cm

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A wooden block is 3 inches on an edge and all of its faces are painted black. If the block is cut such that 27 blocks result, each 1 cubic inch in volume, how many will have no painted faces?


A4

B12

C24

D1

Answer: Option D

Explanation:

Dimension of bigger cube 3-3-3
If we consider first face of dimensions 3*3*1 , it contains 9 cubes and opposite face of this side also contain same.
In middle only 3+2+3 sides are painted.
Middle one is unpainted .
So ans is 1.

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The straight line 2x + 3y = 12 passes through quadrant ?


A1st

B2nd

C3rd

D4th

Answer: Option A

Explanation:

2x/12 + 3y/12=1
x/6 + y/4=1

so (x,y)=(6,4)= 1st quadrant.

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The section of a solid right circular cone by a plane containing vertex and perpendicular to base is an equilateral triangle of side 10 cm. find the volume of the cone?


A221.73 cm3

B223.73 cm3

C228.73 cm3

D226.61 cm3

Answer: Option D

Explanation:

Volume of the cone = 1/3 (PI*R*R*H)

Since the cone is formed from by an equilateral triangle, all sides are equal that is slope = diameter = 10

So, height = (10^2) - (5^2) = ?75 [by hypotenuse theorem]
=> Height = 8.66

Volume = 1/3(8.66*3.14*25)

=> Volume = 226.61 cm^3

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A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to


A10

B50

C60

D20

Answer: Option B

Explanation:

Here is no explanation for this answer

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A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9pi cubic centimeters. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is


A6

B5

C9

D4

Answer: Option A

Explanation:

Here is no explanation for this answer

Workspace

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