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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 the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?

A) 20 B) 36.25
C) 56.25 D) 65
 
Answer & Explanation Answer: C) 56.25

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Q:

Δ XYZ is right angled at Y. If m∠Z = 30°. What is the length of YZ (in cm), if ZX = 9 cm?

A) 6√3 B) 9√3/2
C) 3√3 D) 18
 
Answer & Explanation Answer: B) 9√3/2

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Q:

Find the sum of interior angles of a decagon?

A) 1620° B) 2520°
C) 1800° D) 1440°
 
Answer & Explanation Answer: D) 1440°

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Q:

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

A) 100 B) 400
C) 200 D) 150
 
Answer & Explanation Answer: A) 100

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Q:

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A) 240 B) 120
C) 210 D) 420
 
Answer & Explanation Answer: D) 420

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Q:

If the diameter of a circle is 35 cm, then what will be its circumference (in cm)?

A) 110 B) 220
C) 21 D) 42
 
Answer & Explanation Answer: A) 110

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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:

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold.

 

A) 4929 cub.cm B) 4939 cub.cm
C) 4932 cub.cm D) 4930 cub.cm
 
Answer & Explanation Answer: B) 4939 cub.cm

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