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 Volume and Surface Area Questions

Popular Latest Rated Important Formulae

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:

A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?

A) 4.2 (23) B) 2.1 23
C) 2.1 43 D) 4.2 43
 
Answer & Explanation Answer: B) 2.1 23

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0 1638
Q:

In the given figure,PQ = PS = SR and QPS = 40 deg, then what is the value of QPR (in deg) ?

A) 45 B) 60
C) 75 D) 50
 
Answer & Explanation Answer: C) 75

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1 1632
Q:

ABCD is a rectangle. P is a point on the side AB as shown in the given figure. If Dp = 13, CP = 10

A) √105 B) √133
C) 12 D) 10
 
Answer & Explanation Answer: A) √105

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1 1630
Q:

There are 8 equidistant points A, B, C, D, E, F, G and H (in same order) on a circle. What is the value of ∠FDH (in degrees)?

A) 22.5 B) 45
C) 30 D) 42.5
 
Answer & Explanation Answer: B) 45

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0 1621
Q:

The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area?

A) 300% B) 400%
C) 450% D) 500%
 
Answer & Explanation Answer: A) 300%

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4 1611
Q:

Sum of lengths of all edges of a cube is 84 cm, find its volume?

A) 686 cubic cms B) 343 cubic cms
C) 171.5 cubic cms D) 514.5 cubic cms
 
Answer & Explanation Answer: B) 343 cubic cms

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1 1600
Q:

ΔABC a right angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcentre and AB = 3 cms, BC = 4 cms. The value of BD is

A) 3 cms B) 4 cms
C) 2.5 cms D) 5.5 cms
 
Answer & Explanation Answer: C) 2.5 cms

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0 1587
Q:

A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm2) of each part?

A) 96 + 64√2 B) 80 + 64√2
C) 96 + 48√2 D) 80 + 48√2
 
Answer & Explanation Answer: A) 96 + 64√2

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2 1585