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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:

In the given figure, radius of a circle is 14√2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are 4 identical squares. What is the total area (in sq.cm) of all the small squares ?

A) 31.36 B) 125.44
C) 62.72 D) 156.8
 
Answer & Explanation Answer: A) 31.36

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Q:

In the given figure, PQRS is a square of side 20 cm and SR is extended to point T. If the length of QTis 25 cm, then what is the distance (in cm) between the centers O1 and O2 of the two circles?

A) 5√10 B) 4√10
C) 8√5 D) 16√2
 
Answer & Explanation Answer: A) 5√10

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1 1192
Q:

In the given figure, PQR is an equilateral triangle with side as 12 cm. S and T are the mid points of the sides PQ and PR respectively. What is the area (in sq.cm) of the shaded region?

A) 10√3 B) 12√3
C) 9√3 D) 14√3
 
Answer & Explanation Answer: B) 12√3

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1 1172
Q:

Three consecutive angles of a cycle quadrilateral are in the ratio of 1 : 4 : 5 . The measure of fourth angle is

A) 120° B) 60°
C) 30° D) 80°
 
Answer & Explanation Answer: B) 60°

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1 1168
Q:

A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?

A) 4.2 (23) B) 2.1 23
C) 2.1 43 D) 4.2 43
 
Answer & Explanation Answer: B) 2.1 23

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0 1162
Q:

ΔABC a right angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcentre and AB = 3 cms, BC = 4 cms. The value of BD is

A) 3 cms B) 4 cms
C) 2.5 cms D) 5.5 cms
 
Answer & Explanation Answer: C) 2.5 cms

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0 1132
Q:

In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.

A) 16 cm B) 12 cm
C) 14 cm D) 10 cm
 
Answer & Explanation Answer: C) 14 cm

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1 1124
Q:

Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?

A) a2π+12 B) a
C) a2π2-1 D) πa/2
 
Answer & Explanation Answer: C) a2π2-1

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