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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:

ABCD is a rectangle. P is a point on the side AB as shown in the given figure. If Dp = 13, CP = 10

A) √105 B) √133
C) 12 D) 10
 
Answer & Explanation Answer: A) √105

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1 1884
Q:

In the given figure, MNOP is a parallelogram. PM is extended to Z. OZ intersects MN and PN at Y and X respectively. If OX = 27 cm and XY = 18 cm, then what is the length (in cm) of YZ?

A) 21.4 B) 22.5
C) 23.8 D) 24.5
 
Answer & Explanation Answer: B) 22.5

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0 1880
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 1868
Q:

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?

A) 52 B) 77
C) 128 D) 142
 
Answer & Explanation Answer: C) 128

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0 1866
Q:

In the given figure,PQ = PS = SR and QPS = 40 deg, then what is the value of QPR (in deg) ?

A) 45 B) 60
C) 75 D) 50
 
Answer & Explanation Answer: C) 75

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1 1862
Q:

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

A) 77 B) 154
C) 87 D) 38.5
 
Answer & Explanation Answer: A) 77

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1 1850
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 1840
Q:

PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is 48 cm2 , then what is the length (in cm) of PR ?

A) 12√2 B) 12
C) 24 D) 24√2
 
Answer & Explanation Answer: D) 24√2

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1 1839