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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:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the cube to that of the cylinder ?

A) 4 : 3 B) 21 : 16
C) 14 : 11 D) 45 : 32
 
Answer & Explanation Answer: C) 14 : 11

Explanation:
The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a
Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 =r1
Height of Cylinder = Height of cone = side of cube = a =h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)
VcubeVcylinder = a3πr22h = 14/11
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0 1106
Q:

In the given figure, PQR is a right angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

A) 35.33 B) 37.33
C) 41.33 D) 43.33
 
Answer & Explanation Answer: B) 37.33

Explanation:
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0 1104
Q:

In the given figure, if AD = 12 cm, AE = 8 cm and EC = 14 cm, then what is the value of BD in cm?

A) 50/3 B) 15
C) 8/3 D) 44/3
 
Answer & Explanation Answer: C) 8/3

Explanation:
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2 1102
Q:

Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is

A) 50° B) 60°
C) 80° D) 120°
 
Answer & Explanation Answer: C) 80°

Explanation:
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3 1099
Q:

G is the centroid of the equilateral triangle ABC, if AB = 9cm then AG is equal to

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

Explanation:
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0 1097
Q:

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A) 54 cm B) 9 cm
C) 27 cm D) 13.5 cm
 
Answer & Explanation Answer: C) 27 cm

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0 1096
Q:

Total surface area of a cube is 486 sq cm, find sum of length of all its edges?

A) 216 cms B) 108 cms
C) 54 cms D) 162 cms
 
Answer & Explanation Answer: B) 108 cms

Explanation:
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0 1096
Q:

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 16:9 and PQ = 3.6 cm, then what is the length(in cm) of XY?

A) 4.8 B) 3.2
C) 6.4 D) 8.6
 
Answer & Explanation Answer: C) 6.4

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0 1096