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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:

Find the total surface area (in cm2) of a hemisphere of diameter 21 cm.

 

A) 1039.5   B) 844.5  
C) 637   D) 472
 
Answer & Explanation Answer: A) 1039.5  

Explanation:
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2 5060
Q:

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A) 15360 B) 153600
C) .30720 D) 307200
 
Answer & Explanation Answer: B) 153600

Explanation:

Perimeter = Distance covered in 8 min. = (12000/60) * 8 = 1600m 

Let length = 3x metres and breadth = 2x metres.  

Then, 2(3x + 2x) = 1600 or x = 160.  

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) = 153600 

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0 4944
Q:

Ratio between heights of two cylinder in the ratio 3:5. Their volumes are in the ratio 27:80. Find ratio between their radius ?

A) 1:3 B) 2:1
C) 3:4 D) 4:7
 
Answer & Explanation Answer: C) 3:4

Explanation:

bank

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14 4899
Q:

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10% of its volume is occupied by concrete ?

A) 6000 B) 5400
C) 3800 D) 4700
 
Answer & Explanation Answer: A) 6000

Explanation:

Let 'B' be the nuber of bricks.

=> 10 x 4/100 x 5 x 90/100 = 25/100 x 15/100 x 8/100 x B

=> 10 x 20 x 90 = 15 x 2 x B

=> B = 6000

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5 4883
Q:

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A) 1520 sq.m B) 2420 sq.m
C) 2480 sq.m D) 2520 sq.m
 
Answer & Explanation Answer: D) 2520 sq.m

Explanation:

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. 

Solving the two equations, we get: l = 63 and b = 40. 

Area = (l x b) = (63 x 40) sq.m

= 2520 sq.m

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1 4874
Q:

The volume of a hemisphere is 89.83 cm³. Find its diameter (in cm).

 

A) 3.5 B) 7
C) 14 D) 10.5
 
Answer & Explanation Answer: B) 7

Explanation:
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0 4834
Q:

A Conical tent was erected by the army at a base camp with height 3 m and base diameter 10 m. If every person requires 3.92 cu.m air, then how many persons can be seated in that tent approximately?

A) 20 B) 19
C) 17 D) 22
 
Answer & Explanation Answer: A) 20

Explanation:

Given height of the conical tent = 3 m

Diameter = 10 => Radius = D/2 = 10/2 = 5 m 

Now, as the tent is in the conical form

Volume of the conical tent = πr2h3 

=> (22 x 5 x 5 x 3) / (7 x 3) 

= 22 x 25/7 

= 78.54 cu.m 

Given each person requires 3.92 cu.m of air 

=> Number of persons can be seated in the tent = 78.54/3.92 = 20.03 =~ 20

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17 4818
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 4816