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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:

In the figure ∠AMB = 130°, then what is the value (in deg) of ∠ABQ?

 

A) 40 B) 50
C) 60 D) 90
 
Answer & Explanation Answer: B) 50

Explanation:
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3 6931
Q:

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8m, the volume of the box (in m3) is:

A) 4830 B) 5120
C) 6420 D) 8960
 
Answer & Explanation Answer: B) 5120

Explanation:

ke

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4 6897
Q:

Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.

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

Explanation:

 4×3.14×r2 : 4×3.14×r2 = 1 : 2  

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10 6852
Q:

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A) 2.91 m B) 3 m
C) 5.82 m D) None of these
 
Answer & Explanation Answer: B) 3 m

Explanation:

Area of the park = (60 x 40) = 2400 sq.m  

Area of the lawn = 2109  sq.m 

Area of the crossroads = (2400 - 2109) = 291 sq.m   

 

Let the width of the road be x metres. Then,   

60x + 40x - (x * x) = 291  

=>(x * x) - 100x + 291 = 0    

=>(x - 97)(x - 3) = 0  

=>x=3

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1 6745
Q:

The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.

A) 50% B) 40%
C) 30% D) 20%
 
Answer & Explanation Answer: A) 50%

Explanation:

Let l, b the sides of the base, so that the area of the base = lb
remains constant.
Let ‘h’ be the height of the solid.
Volume of the solid, V = l× b× h.
Since the volume is to be increased by 50%

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8 6739
Q:

Consider the following statements:

1) The number of circles that can be drawn through three non-collinear points is infinity.

2) Angle formed in minor segment of a circle is acute.

Which of the above statements is/are correct?

A) 1 only B) 2 only
C) Both 1 and 2 D) Neither 1 nor 2
 
Answer & Explanation Answer: D) Neither 1 nor 2

Explanation:
(1)
Only one circle can be drawn through 3 non collinear points 
Angle in the minor segment is always obtuse
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1 6608
Q:

If the radius of base and height of a cone are increased by 10%, find the percentage of increase of its volume

A) 33.5% B) 33.1%
C) 32.1% D) 53.1%
 
Answer & Explanation Answer: B) 33.1%

Explanation:

v1= 13πr12h1

 

v2=13πr22h2

 

% Increase in volume = (V2-V1) / (V2*100)

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9 6550
Q:

What part of the volume of a cube is the pyramid whose base is the base of then cube and whose vertex is the center of the cube?

A) 4:1 B) 5:1
C) 6:1 D) 7:1
 
Answer & Explanation Answer: C) 6:1

Explanation:

Volume of the cube/volume of pyramid=a313a2×a2

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1 6517