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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 line segment AB intersects the straight line CD at B; AB will be smallest when ∠ ABD (in degrees) is

A) 30 B) 60
C) 90 D) 45
 
Answer & Explanation Answer: C) 90

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Q:

How many balls of radius 2 cm can be made by melting a bigger ball of diameter 16 cm? (Take π = 22/7)

A) 64 B) 128
C) 32 D) 96
 
Answer & Explanation Answer: A) 64

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1 1536
Q:

If PA and PB are tangents to the circle with centre O such that ∠APB=50°, then the ∠OAB=

A) 25° B) 30°
C) 40° D) 50°
 
Answer & Explanation Answer: A) 25°

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0 1535
Q:

If curved surface area of a cylinder is 1320 sq cm and height is 10 cm, find its radius?

A) 21 cm B) 42 cm
C) 63 cm D) 10.5 cm
 
Answer & Explanation Answer: A) 21 cm

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1 1532
Q:

The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :

A) 4:7 B) 7:4
C) 28:27 D) 27:28
 
Answer & Explanation Answer: D) 27:28

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1 1530
Q:

If PA and PB are two tangents to a circle with centre O such that ∡APB = 80°. Then ∡AOP = 

A) 40° B) 50°
C) 60° D) 70°
 
Answer & Explanation Answer: B) 50°

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0 1529
Q:

The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is 15√3 sq cm, what is the area of the equilateral triangle?

A) 45/√2 sq cm B) 45√2 sq cm
C) 45 sq cm D) 45/2 sq cm
 
Answer & Explanation Answer: D) 45/2 sq cm

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1 1528
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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