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 a10cm x 4cm x 3cm brick

A) 84 B) 124
C) 164 D) 180
 
Answer & Explanation Answer: C) 164

Explanation:

surface area = [2(10*4 + 4*3 + 10*3)]sq.cm = 164 sq.cm

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22 15474
Q:

The curved surface area of a cylindrical pillar is 264 sq.m and its volume is 924 cub.m. Find the ratio of its diameter to its height

A) 3 : 7 B) 7 : 3
C) 6 : 7 D) 7 : 6
 
Answer & Explanation Answer: B) 7 : 3

Explanation:

πr2h2πr2h = 924264  

=> r = (24/364) x 2 = 7m 

2πrh = 264   h = (264 × 722×12 ×17) = 6m   

Required Rato =2r/h  =14/6 = 7:3

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21 15438
Q:

Which of the following statement is CORRECT about the tangents?

 

A) The tangents drawn at the end of diameter of a circle are parallel to each other.   B) The line segment which joins the point of contact of two parallel tangents to the circle is the diameter of the circle.  
C) Tangents drawn from the external points subtends equal angle at the center.   D) All option are correct.  
 
Answer & Explanation Answer: D) All option are correct.  

Explanation:
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1 15023
Q:

The cost of the paint is rs.36.50 per kg. if 1kg of paint covers 16sq.ft, how much will it cost to paint outside of a cube having 8 feet each side

A) Rs.962 B) Rs.672
C) Rs.546 D) Rs.876
 
Answer & Explanation Answer: D) Rs.876

Explanation:

surface area of a cube= 6 x (8 x 8) = 384 sq.ft  

quantity of paint required=(384/16)=24kg  

cost of painting= 36.5 x 24 = Rs.876

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12 14878
Q:

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.

A) 3:1 B) 2:1
C) 4:1 D) 5:1
 
Answer & Explanation Answer: A) 3:1

Explanation:

v1v2=r12Hr22H

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28 14689
Q:

The total surface area of a cube is 253.5 sq.cm. Find its side (in cm).

 

A) 7.5 B) 5.5
C) 6.5 D) 8.5
 
Answer & Explanation Answer: C) 6.5

Explanation:
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0 14489
Q:

The capacity of a tank of dimensions (8m x 6m x 2.5m)is

A) 120 litres B) 1200 litres
C) 12000 litres D) 120000 litres
 
Answer & Explanation Answer: D) 120000 litres

Explanation:

capacity of a tank = volume of tank 

= [ (8 x 100) x (6 x 100) x (2.5 x 100) ]/ 1000 litres 

= 120000 litres

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12 14474
Q:

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface

A) 40pi sq.m B) 50pi sq.m
C) 60pi sq.m D) 70pi sq.m
 
Answer & Explanation Answer: C) 60pi sq.m

Explanation:

ke

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