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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:

The radius of a wire is decreased to one-third. If volume remains the same, length will increase by

A) 1.5 times B) 3 times
C) 6 times D) 9 times
 
Answer & Explanation Answer: D) 9 times

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Q:

In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

A) 3 cm B) 4 cm
C) 6 cm D) 12 cm
 
Answer & Explanation Answer: C) 6 cm

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Q:

What is the diameter (in cm) of a sphere of surface area 6.16 sq cm?

A) 1.4 B) 0.7
C) 2.8 D) 2.1
 
Answer & Explanation Answer: A) 1.4

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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:

A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

A) 26.46 cm B) 39.69 cm
C) 13.23 cm D) 52.92 cm
 
Answer & Explanation Answer: C) 13.23 cm

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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:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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Q:

A cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

A) 11.76 cm B) 17.64 cm
C) 23.52 cm D) 5.88 cm
 
Answer & Explanation Answer: D) 5.88 cm

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