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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 regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A) 24 B) 20
C) 27 D) 28
 
Answer & Explanation Answer: A) 24

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Q:

The radius of a hemisphere is 7 cm, find its volume?

A) 718.67 cubic cm B) 1437.34 cubic cm
C) 239.56 cubic cm D) 359.34 cubic cm
 
Answer & Explanation Answer: A) 718.67 cubic cm

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Q:

An angle is greater than its complementary by 20°. What will be the measure of the angle?

A) 55° B) 35°
C) 100° D) 80°
 
Answer & Explanation Answer: A) 55°

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Q:

In a circle, a chord, 5√2 cm long, makes a right angle at the centre. Then the length of the radius of the circle will be

A) 2.5 cm B) 5 cm
C) 7.5 cm D) 10 cm
 
Answer & Explanation Answer: B) 5 cm

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Q:

What is the reflection of the point (1 , 2) in the line y = 3?

A) (1, -4) B) (1, 4)
C) (-1, -4) D) (-1, 4)
 
Answer & Explanation Answer: B) (1, 4)

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Q:

In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

A) 107.5 B) 112.5
C) 117.5 D) 122.5
 
Answer & Explanation Answer: B) 112.5

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Q:

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

A) 1 B) ∏/2
C) ∏/3 D) ∏/4
 
Answer & Explanation Answer: C) ∏/3

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Q:

A cylindrical capsule has hemispherical ends of the radii equal to radius of the cylindrical part. If length of the capsule is 40 m and radius 6 m, what is the total surface area of this capsule?

A) 3017.14 sq mts B) 4525.71 sq mts
C) 1508.57 sq mts D) 754.29 sq mts
 
Answer & Explanation Answer: C) 1508.57 sq mts

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