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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:

BD and CE are two medians of the triangle ABC. If EO = 7 cm, then the length of CE is

A) 28 cm B) 14 cm
C) 21 cm D) 35 cm
 
Answer & Explanation Answer: C) 21 cm

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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 1187
Q:

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?

A) 12 B) 14
C) 16 D) 28
 
Answer & Explanation Answer: D) 28

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Q:

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

A) 493 B) 7
C) 14 D) 983
 
Answer & Explanation Answer: B) 7

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Q:

Find the circumference (in cm) of a circle of radius 17.5 cm.

A) 140 B) 110
C) 38 D) 76
 
Answer & Explanation Answer: B) 110

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Q:

The perimeter and the breadth of a rectangle are 44 cm and 10 cm respectively. Find its area (in cm2).

A) 60 B) 240
C) 120 D) 180
 
Answer & Explanation Answer: C) 120

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Q:

ABCD is a trapezium in which AB is parallel to CD and AB = 4(CD). The diagonals of the trapezium intersects at O. What is the ratio of area of triangle DCO to the area of the triangle ABO?

A) 1 : 4 B) 1 : 2
C) 1 : 8 D) 1 : 16
 
Answer & Explanation Answer: D) 1 : 16

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0 1182
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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