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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:

What is the sum of the measures of all the interior angles of a regular polygon of 5 sides?

A) 720 B) 1080
C) 1260 D) 540
 
Answer & Explanation Answer: D) 540

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Q:

A circle has its centre at O . A tangent drawn from a point P , which is situated outside the circle, touches the circle at A. If PA = 4 cm & PO=5 cm, then the length of the radius of the circle is

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

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Q:

The line parallel to the BC of the triangle ABC divides the other two sides at the point D and E in such a way that AB=3AD. Calculate the ratio of DE and BC.

 

A) 1:6 B) 1:4
C) 1:3 D) 3:1
 
Answer & Explanation Answer: C) 1:3

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Q:

What is the reflection of the point (-1 , 3) in the line x = -4?

A) (-7 ,-3) B) (-7 ,3)
C) (7 ,-3) D) (7 ,3)
 
Answer & Explanation Answer: B) (-7 ,3)

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Q:

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

A) √2 B) 2
C) 1/√2 D) 1/2
 
Answer & Explanation Answer: A) √2

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Q:

The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

A) 2 : 1 B) √2 : 1
C) 23 : 1 D) 33 : 23
 
Answer & Explanation Answer: C) 23 : 1

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Q:

An angle is greater than its complementary angle by 40°. Find the measure of the angle?

A) 25° B) 65°
C) 130° D) 50°
 
Answer & Explanation Answer: B) 65°

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Q:

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A) 60 sq cm B) 16 sq cm
C) 96 sq cm D) 21 sq cm
 
Answer & Explanation Answer: C) 96 sq cm

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