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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 tangents PA and PB are drawn to a circle of centre O in such a way that angle AOB = 120 deg. Calculate the value of angle APB.

A) 40 deg B) 50 deg
C) 60 deg D) 80 deg
 
Answer & Explanation Answer: C) 60 deg

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Q:

The copper wire when bent in the form of a square encloses an area of 121 cub.cm. If the same wire is bent into the form of a circle, find the area of the circle.

A) 154 sq.cm B) 153 sq.cm
C) 155 sq.cm D) 150 sq.cm
 
Answer & Explanation Answer: A) 154 sq.cm

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Q:

The base and hypotenuse of a right angled triangle is 12 cm and 5 cm respectively. Find the circum-radius (in cm) of the triangle.

 

A) 5 B) 6
C) 6.5 D) 7
 
Answer & Explanation Answer: C) 6.5

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Q:

What is the slope of the line parallel to the line passing through the points (6,­3) and (2,­1)?

A) -1/2 B) -1
C) 2 D) 1
 
Answer & Explanation Answer: A) -1/2

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Q:

Find the total surface area (in cm2) of a cube of side 3.5 cm.

A) 91.7 B) 64
C) 88 D) 73.5
 
Answer & Explanation Answer: D) 73.5

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Q:

If any two sides of a triangle are divided by the line in the same ratio, then the line must be _________________ to the third side of the triangle.

A) equal B) parallel
C) perpendicular D) non parallel
 
Answer & Explanation Answer: B) parallel

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Q:

If the measure of the interior angle of a regular polygon is 100 deg greater than the measure of its exterior angle then how many sides does it have?

 

A) 10 B) 12
C) 9 D) 15
 
Answer & Explanation Answer: C) 9

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Q:

In a triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is :

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

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