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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:

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°? 

A) 8√3 cm B) 16√2 cm
C) 8 cm D) 16√3 cm
 
Answer & Explanation Answer: B) 16√2 cm

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Q:

In a triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is :

A) 3 cm B) 2 cm
C) 4 cm D) 1 cm
 
Answer & Explanation Answer: A) 3 cm

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Q:

If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm and its area is 54 cm². Find the distance between its parallel sides (in cm).

A) 6 B) 3
C) 12 D) 9
 
Answer & Explanation Answer: A) 6

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Q:

What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

A) 2 B) 4
C) 3 D) 6
 
Answer & Explanation Answer: B) 4

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0 933
Q:

ΔABC is right angled at B. BD is the altitude. AD is 8 cm and DC is 50 cm. What is the length of BD?

A) 25 cm B) 20 cm
C) 16 cm D) 15 cm
 
Answer & Explanation Answer: B) 20 cm

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0 932
Q:

Slope of the side DA of the rectangle ABCD is 1/3. What is the slope of the side AB?

A) 3 B) 1/3
C) -­1/3 D) -3
 
Answer & Explanation Answer: D) -3

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0 931
Q:

The lengths of the two diagonals of a rhombus are 7 cm and 24 cm. Find the length of its perimeter (in cm).

A) 25 B) 100
C) 75 D) 50
 
Answer & Explanation Answer: D) 50

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1 931
Q:

ΔABC is similar to ΔDEF. Length of AB is 12 cm and length of the corresponding side DE is 8 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

A) 9:4 B) 4:9
C) 3:2 D) 2:3
 
Answer & Explanation Answer: C) 3:2

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0 930