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 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 = (πrl)sq.units 

 

4. Total surface area = (πrl+πr2)sq.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 the volume of the cube is 729 cm3, then the surface area of the cube will be

A) 486 sq.cm B) 456 sq.cm
C) 446 sq.cm D) 476 sq.cm
 
Answer & Explanation Answer: A) 486 sq.cm

Explanation:

volume = a3 = 729;

=> a = 9

 

surface area= 6a2 =  (6 x 9 x 9) = 486 sq.cm

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19 15991
Q:

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

A) 344.35 sq.cm B) 462 sq.cm
C) 498.35 sq.cm D) None of these
 
Answer & Explanation Answer: C) 498.35 sq.cm

Explanation:

h = 14 cm, r = 7 cm.  

So, l =[72+142] = 245 = 75cm   

Total surface area = πrl+πr2 = 227×7×75 + 227×7×7 

=154(5+1) 

= (3.236 x 154) sq.cm   

= 498.35 sq.cm

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6 15781
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 15515
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 15454
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 15047
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 14940
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 14712
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 14636