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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:

If in-radius of an equilateral triangle is 3 cm. Calculate the perimeter (in m) of the equilateral triangle.

 

A) 6√3 B) 3√3
C) 12√3 D) 18√3
 
Answer & Explanation Answer: D) 18√3

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Q:

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is

A) 27:20 B) 20:27
C) 4:9 D) 9:4
 
Answer & Explanation Answer: B) 20:27

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Q:

The amount of extension in a spring is proportional to the weight hung on it. If the weight of 5 kgs produces an extension of 0.4 cm, what weight would produce an extension of 5cm?

A) 6.25kgs B) 62.5kgs
C) 4kgs D) 40kgs
 
Answer & Explanation Answer: B) 62.5kgs

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Q:

The volume of a cuboid is 320 cubic cm. Find its total surface area if its length and breadth are 10 cm and 8 cm respectively?

A) 608 sq cms B) 304 sq cms
C) 152 sq cms D) 456 sq cms
 
Answer & Explanation Answer: B) 304 sq cms

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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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Q:

The length of the two adjacent sides of a rectangle inscribed in a circle are 5 cm and 12 cm respectively. Then the radius of the circle will be

A) 6 cm B) 6.5 cm
C) 8 cm D) 8 .5 cm
 
Answer & Explanation Answer: B) 6.5 cm

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Q:

The length, breadth and height of a cuboid are 10 cm, 6 cm and 4 cm respectively. What is the total surface area?

A) 248 sq cms B) 496 sq cms
C) 124 sq cms D) 372 sq cms
 
Answer & Explanation Answer: A) 248 sq cms

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0 978
Q:

What is the slope of the line 2x + 3y = 12?

A) 2/3 B) 3/2
C) -3/2 D) -2/3
 
Answer & Explanation Answer: D) -2/3

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