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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:

What is the total surface area (in sq cm) of a hollow cylinder open at both ends, if its length is 22 cm, external radius is 7 cm and thickness is 1 cm? (Take π = 22/7)

A) 1879.43 B) 3758.86
C) 939.715 D) 2819.145
 
Answer & Explanation Answer: A) 1879.43

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0 1097
Q:

The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?

A) a(√2 –1) B) a(√3 –1)
C) a/√2+2 D) a/3
 
Answer & Explanation Answer: A) a(√2 –1)

Explanation:

Since we are forming a regular octagon

so AE = AL = FB = BG and so on

So AE = SB = x/√2

AE + EF + FB = side of square = a (Given)

So x/√2 + x + x/√2 = a

X = a/(√2+1) = a(√2 -1)

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0 1096
Q:

The volume of a right circular cone, whose radius of the base is same as its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is

 

A) 33 : 23 B) 2 : 1
C) 1 : 1 D) 43 : 1
 
Answer & Explanation Answer: D) 43 : 1

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Q:

An angle is smaller than its supplementary by 30°. What is the measure of the angle?

A) 75° B) 105°
C) 60° D) 30°
 
Answer & Explanation Answer: A) 75°

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0 1095
Q:

PQR is a right angled triangle in which ∠R = 90°. If RS ⊥ PQ, PR = 3 cm and RQ = 4 cm, then what is the value of RS (in cm)?

A) 12/5 B) 36/5
C) 5 D) 2.5
 
Answer & Explanation Answer: A) 12/5

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0 1094
Q:

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

A) 10 units B) 8 units
C) 6 units D) 4 units
 
Answer & Explanation Answer: D) 4 units

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0 1094
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 1091
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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