Volume and Surface Areas Questions

Q:

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

A) 125% B) 150%
C) 175% D) 110%
 
Answer & Explanation Answer: A) 125%

Explanation:

Let the edge = a cm 

So increase by 50 % =  = 

Total surface Area of original cube = 

TSA of new cube = 

==  

Increase in area =  =

  Increase % = = 125%

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58 12519
Q:

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A) 30 B) 40
C) 10 D) 20
 
Answer & Explanation Answer: B) 40

Explanation:

Volume of the block = (6 x 12 x 15) \inline \fn_jvn cm^3 = 1080 \inline \fn_jvn cm^3

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

                                          = 3 cm.

Volume of this cube  = (3 x 3 x 3) \inline \fn_jvn cm^3 = 27 \inline \fn_jvn cm^3

Number of cubes = = 40.

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Q:

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

A) 36 B) 232
C) 216 D) 484
 
Answer & Explanation Answer: C) 216

Explanation:

number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216

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Q:

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A) 40cm B) 30cm
C) 20cm D) 10cm
 
Answer & Explanation Answer: A) 40cm

Explanation:

Let the breadth of the wall be x metres.

Then, Height = 5x metres and Length = 40x metres.

x * 5x * 40x = 12.8

=>\inline \fn_jvn x^3=\frac{12.8}{200}=\frac{128}{2000}=\frac{64}{1000}

=>\inline \fn_jvn x=\frac{4}{10}m

=>\inline \fn_jvn x=\frac{4}{10}\times 100=40cm

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Q:

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A) 49 B) 50
C) 53.5 D) 55
 
Answer & Explanation Answer: A) 49

Explanation:

Area of the wet surface = [2(lb + bh + lh) - lb]

= 2(bh + lh) + lb

= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]

= 49

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