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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 a triangle the length of the side opposite the angle which measures 60° is 15 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 15 cm B) (15√3)/2 cm
C) 10√3 cm D) 10 cm
 
Answer & Explanation Answer: C) 10√3 cm

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Q:

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold.

 

A) 4929 cub.cm B) 4939 cub.cm
C) 4932 cub.cm D) 4930 cub.cm
 
Answer & Explanation Answer: B) 4939 cub.cm

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Q:

The total surface area of a cube is 181.5 cm². Find its side (in cm).

A) 6.5 B) 4.5
C) 7.5 D) 5.5
 
Answer & Explanation Answer: D) 5.5

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Q:

 Find the volume (in cm3) of a hemisphere of diameter 42 cm.

A) 17832 B) 153512
C) 13858 D) 19404
 
Answer & Explanation Answer: D) 19404

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0 450
Q:

A triangle is circumscribed on the circle of centre O in such a way that sides AB = 12 cm, BQ = 7 cm and CQ = 5 cm. Calculate the lengtth (in cm) of side AC.

A) 8 B) 10
C) 12 D) 14
 
Answer & Explanation Answer: B) 10

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0 447
Q:

The length of the diameter of the circle is 10 cm and length of the chord drawn in a circle is 6 cm. Find the distance (in cm) of chord from the center.

 

A) 10 B) 8
C) 6 D) 4
 
Answer & Explanation Answer: D) 4

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Q:

The line parallel to the BC of the triangle ABC divides the other two sides at the point D and E in such a way that AB=3AD. Calculate the ratio of DE and BC.

 

A) 1:6 B) 1:4
C) 1:3 D) 3:1
 
Answer & Explanation Answer: C) 1:3

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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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