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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 cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

A) 384.13 sq cm B) 576.19 sq cm
C) 192.06 sq cm D) 288.1 sq cm
 
Answer & Explanation Answer: B) 576.19 sq cm

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0 1007
Q:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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0 1005
Q:

For the figure given below, find the value (in degrees) of 2∠A + ∠B.

A) 180° B) 202.5°
C) 250° D) 279°
 
Answer & Explanation Answer: B) 202.5°

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0 1003
Q:

The co-ordinates of the centroid of a triangle ABC are (2 , 2). What are the co-ordinates of vertex C if co-ordinates of A and B are (7 , -1) and (1 , 2) respectively?

A) (-2 , 5) B) (2 , 5)
C) (-2 , -5) D) (2 , -5)
 
Answer & Explanation Answer: A) (-2 , 5)

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0 1002
Q:

The triangle in which the orthocenter, circumcentre, Incenter and the centroid coincide each other at a point is known as _____________.

A) isosceles triangle B) equilateral triangle
C) right angled triangle D) obtuse angled triangle
 
Answer & Explanation Answer: B) equilateral triangle

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0 1001
Q:

The whole surface area of a pyramid whose base is a regular polygon is 340 cm2 and area of its base is 100 cm2 . Area of each lateral face is 30 cm2. Then the number of lateral faces is

A) 8 B) 9
C) 7 D) 10
 
Answer & Explanation Answer: A) 8

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0 1000
Q:

The volume of a sphere is 179.67 cub.cm. Find its diameter (in cm).

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

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0 997
Q:

 In ΔDEF measure of angle E is 90 deg. If tanD = 4/3, and DE = 6cm, then what is the length (in cm) of side EF?

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

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0 996