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:

Find the  surface area of a cuboid 16 m long, 14 m broad and 7 m high

A) 868 sq.cm B) 920 sq.cm
C) 727 sq.cm D) 900 sq.cm
 
Answer & Explanation Answer: A) 868 sq.cm

Explanation:

 Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] sq.cm

= (2 x 434)sq.cm  = 868 sq.cm

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14 14358
Q:

The diagonal of a cube is 63 cm. Find its  surface area

A) 216 sq.cm B) 316 sq.cm
C) 416 sq.cm D) 516 sq.cm
 
Answer & Explanation Answer: A) 216 sq.cm

Explanation:

Let the edge of the cube be a.  

 so, the diagonal  a3 = 63    

=> a=6 

 Surface area = 6a2 = 6 x 6 x 6 = 216 sq.cm

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37 14196
Q:

What is the simplified form of 64288 ?

 

A) 23 B) 1/2
C) 23 D) 33
 
Answer & Explanation Answer: A) 23

Explanation:
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0 14105
Q:

∆PQR is right angled at Q. If m∠P = 60 deg, then find the value of (secR + 1/2).

 

A) (2√2+√3)/2   B) (√3+4)/2√3
C) √3+2   D) 5/6
 
Answer & Explanation Answer: B) (√3+4)/2√3

Explanation:
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0 13982
Q:

What is the measure of an interior angle of a regular polygon of 8 sides?

 

A) 140 B) 144
C) 135 D) 150
 
Answer & Explanation Answer: C) 135

Explanation:
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1 13332
Q:

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A) 75 cubic meter B) 750 cubic meter
C) 7500 cubic meter D) 75000 cubic meter
 
Answer & Explanation Answer: B) 750 cubic meter

Explanation:

1 hectare = 10,000 Sq.m

So, Area = (1.5 x 10000) Sq.m

Depth = 5/100 m = 1/20 m

Therefore, Volume = Area X Depth = 15000 x (1/20)= 750 cu.m

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29 13188
Q:

What is the measure of an exterior angle of a regular polygon of 5 sides?

 

A) 72 B) 60
C) 45 D) 40
 
Answer & Explanation Answer: A) 72

Explanation:
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0 12870
Q:

How many iron rods, each of length 7 mts and diameter 2 cms can be made out of 0.88 cubic metre of iron ?

A) 500 B) 600
C) 400 D) 300
 
Answer & Explanation Answer: C) 400

Explanation:

Given length of iron rod =7 mts and  and diameter of rod = 2 cms 

=> r = 1/100 mts

Therefore,  Volume of one rod = πr2h cu. m =  227×11002×7cu. m = 115000 cu. m

Given volume of iron = 0.88 cu. m 

Therefore, Number of rods = 0.88×500011 = 400.

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Exam Prep: CAT
Job Role: Bank PO

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