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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:

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameters of the frustum are 5cm and 2cm, the height of the entire shuttle cock is 7cm. Find the external surface area.

A) 80 sq.cm B) 73.38 sq.cm
C) 74.29 sq.cm D) 74.30 sq.cm
 
Answer & Explanation Answer: A) 80 sq.cm

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Q:

Find the in-radius (in cm) of an equilateral triangle whose sides are 6 cm each.

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

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Q:

 The line bisecting all the three angles of a triangle meets at a common point. This point is known as ______________.

A) circum-center B) centroid
C) orthocenter D) in-center
 
Answer & Explanation Answer: D) in-center

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Q:

What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

A) 2 B) 4
C) 3 D) 6
 
Answer & Explanation Answer: B) 4

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Q:

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR?

A) 30 B) 45
C) 60 D) 90
 
Answer & Explanation Answer: D) 90

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Q:

Consider the following figure shown below and choose which of the following equation is correct about the similarity of both triangles?

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

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Q:

The minimum number of straight lines required to construct the given figure is ___.

A) 11 B) 12
C) 9 D) 10
 
Answer & Explanation Answer: A) 11

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Q:

In ΔPQR measure of angle Q is 90 deg. If tanP = 24/7, and PQ = 14cm, then what is the length (in cm) of side QR?

 

A) 50 B) 20
C) 26 D) 48
 
Answer & Explanation Answer: D) 48

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