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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:

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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0 814
Q:

If the side of the equilateral triangle is 8√3 cm, then what is the length (in cm) of the in radius of the triangle?

A) 2 B) 4
C) 8√3 D) 16√3
 
Answer & Explanation Answer: B) 4

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0 813
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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0 811
Q:

Find the total surface area (in cm2) of a right circular cone of diameter 21 cm and slant height 11 cm.

A) 467.5 B) 384
C) 724 D) 709.5
 
Answer & Explanation Answer: D) 709.5

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0 811
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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0 809
Q:

The total surface area of a hemisphere is 166.32 sq cm, find its curved surface area?

A) 221.76 sq cm B) 36.96 sq cm
C) 110.88 sq cm D) 55.44 sq cm
 
Answer & Explanation Answer: C) 110.88 sq cm

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0 809
Q:

In a triangle the length of the side opposite the angle which measures 30 degree is 9√3 cm, what is the length of the side opposite to the angle which measures 60 degree?

A) 27 cm B) 9 cm
C) 12√3 cm D) (15√3)/2 cm
 
Answer & Explanation Answer: A) 27 cm

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0 808
Q:

In a triangle ABC, if ∡A +∡C = 140° and ∡A + 3∡B = 180°, then ∡A is equal to

A) 80° B) 40°
C) 60° D) 20°
 
Answer & Explanation Answer: C) 60°

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0 807