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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:

One internal angle of a rhombus of side 12 cm is 120°. What is the length of its longer diagonal?

A) 6√3 cm B) 12√2 cm
C) 6√2 cm D) 12√3 cm
 
Answer & Explanation Answer: D) 12√3 cm

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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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Q:

The total surface area of a cube is 337.5 cm². Find its side (in cm).

A) 8.5 B) 6.5
C) 5.5 D) 7.5
 
Answer & Explanation Answer: D) 7.5

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Q:

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3 B)  6√3
C) 6 D) 3
 
Answer & Explanation Answer: A) 3√3

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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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Q:

An arc of 30° in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is

A) 3° B) 4°
C) 5° D) 6°
 
Answer & Explanation Answer: C) 5°

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Q:

The area of a semicircle is 1925 cm2. Calculate its perimeter (in cm).

A) 360 B) 80
C) 160 D) 180
 
Answer & Explanation Answer: D) 180

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Q:

The surface area of a sphere is 5544 cm2. Find its diameter (in cm).

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

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