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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 right circular conical structure stands on a circular base of 21m diameter and is 14m in height. The total cost of colour washing for its curved surface at Rs. 6 per sq. m. is
(Take Π = 22/7 )

A) 4365 B) 4465
C) 3465 D) 3365
 
Answer & Explanation Answer: C) 3465

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0 1357
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 1355
Q:

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area (in sq cm) of the circle?

A) 308 B) 462
C) 154 D) 616
 
Answer & Explanation Answer: C) 154

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0 1352
Q:

The diagonal of a square is 10 cm. What is the length (in cm) of its side?

A) 5 B) 5√2
C) 10√2 D) 5/√2
 
Answer & Explanation Answer: B) 5√2

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0 1350
Q:

What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are 120 sq.cm and 8 cm respectively ?

A) 34 B) 17
C) 15 D) 30
 
Answer & Explanation Answer: B) 17

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1 1349
Q:

Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is

A) 7.5 cm B) 9 cm
C) 8 cm D) 10 cm
 
Answer & Explanation Answer: B) 9 cm

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0 1349
Q:

The surface area of a sphere is 5544 sq.cm. Find its diameter (in cm).

A) 42 B) 21
C) 84 D) 63
 
Answer & Explanation Answer: A) 42

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1 1348
Q:

In ΔPQR, L and M are two points on the sides PQ and PR respectively such that LM II QR. If PL=2cm; LQ=6cm and PM=1.5 cm, then MR in cm is

A) 0.5 B) 4.5
C) 9 D) 8
 
Answer & Explanation Answer: B) 4.5

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0 1347