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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:

The surface area of a sphere is 2464 cm². Find its diameter (in cm).

A) 14 B) 56
C) 28 D) 42
 
Answer & Explanation Answer: C) 28

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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:

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:

In ΔABC, ∠B is right angle, D is the mid point of the side AC. If AB = 6 cm, BC = 8cm, then the length of BD is

A) 4 cm B) 5 cm
C) 8 cm D) 12 cm
 
Answer & Explanation Answer: B) 5 cm

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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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Q:

Which of the following is the CORRECT option for the triangles having sides in the ratio of 3:4:6?

A) Acute angled B) Obtuse angled
C) Right angled D) Either acute or right angled
 
Answer & Explanation Answer: B) Obtuse angled

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Q:

The curved surface area of a hemisphere is 27.72 sq cm and volume is 19.404 cubic cm, find its radius?

A) 4.2 cm B) 2.1 cm
C) 0.7 cm D) 1.05 cm
 
Answer & Explanation Answer: B) 2.1 cm

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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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