Volume and Surface Area Questions

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

 

 

I. CUBOID

   Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =l2+b2+h2 units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

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 % = a + a/2 = 3a/2  

Total surface Area of original cube = 6a2  

TSA of new cube = 63a22 =69a24=  13.5a2   

Increase in area = 13.5a2-6a2 =7.5a2  

 7.5a2 Increase % =7.5a26a2×100 = 125%

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270 52843
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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71 20581
Q:

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

A) 12 pi cub.cm B) 15 pi cub.cm
C) 16 pi cub.cm D) 20 pi cub.cm
 
Answer & Explanation Answer: A) 12 pi cub.cm

Explanation:

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39 17850
Q:

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A) 720 B) 900
C) 1200 D) 1800
 
Answer & Explanation Answer: C) 1200

Explanation:

ke

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32 17334
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) cu.cm = 1080 cu.cm 

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) cu.cm = 27 cu.cm 

Number of cubes =108027 = 40.

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37 17163
Q:

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

A) 486 B) 586
C) 686 D) 786
 
Answer & Explanation Answer: A) 486

Explanation:

Volume of new cube =  13+63+83cm3729cm3  

Edge of new cube = 7293 = 9cm

Surface area of the new cube = ( 6 x 9 x 9) sq.cm = 486 sq.cm

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22 13622
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]m2  

= 49m2

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33 12624
Q:

The diagonal of a rectangle is sqrt(41) cm.  and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 9 cm B) 18 cm
C) 20 cm D) 41 cm
 
Answer & Explanation Answer: B) 18 cm

Explanation:

l2+b2 = diagonal2=40

Also, lb=20

 

l+b2=l2+b2+2lb = 41 + 40 =81 

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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10 12195