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 Volume and Surface Area Questions

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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 14728
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 14601
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 14007
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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22 13663
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 13415
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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11 13129
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 13111
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 13018