Volume and Surface Area Questions

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:

Find the total surface area (in cm2) of a cuboid of length, breadth and height of 10.5 cm, 8 cm and 9 cm respectively.

A) 607 B) 767
C) 769 D) 501
 
Answer & Explanation Answer: D) 501

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Q:

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

A) AP = BQ B) AP | BQ
C) AP || BQ D) AP = 1⁄2 BQ
 
Answer & Explanation Answer: C) AP || BQ

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Q:

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is

A) 27:20 B) 20:27
C) 4:9 D) 9:4
 
Answer & Explanation Answer: B) 20:27

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Q:

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

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

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Q:

A wheel has diameter 84 cm. The number of complete revolution it will take to cover 792 m is

A) 330 B) 300
C) 320 D) 350
 
Answer & Explanation Answer: B) 300

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Q:

What is the slope of the line perpendicular to the line passing through the points (­6,3) and (2,7)?

A) -2 B) 2
C) 1/2 D) -1/2
 
Answer & Explanation Answer: A) -2

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Q:

Which of the following condition is True about the similarity of triangle ABC & DEF given below?

A) 1 B) 2
C) 3 D) none
 
Answer & Explanation Answer: A) 1

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Q:

If the edge of a cube is increased by 2 cm, the volume will increase by 488 cub.cm. What then will be the length of each edge of the cube?

A) 6 cm B) 8 cm
C) 9 cm D) 7 cm
 
Answer & Explanation Answer: B) 8 cm

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