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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 measures of the four angles of a quadrilateral are in the ratio 1:2:4:5. What is the measure of the biggest angle?

A) 120° B) 30°
C) 60° D) 150°
 
Answer & Explanation Answer: D) 150°

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Q:

The triangle ABC and DEF are similar to each other. The measure of the angle A and E is 67 and 83 degree respectively. What is the value of angle C?

A) 20°   B) 30°
C) 40° D) 50°
 
Answer & Explanation Answer: B) 30°

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Q:

The sum of the lengths of the edges of a cube is equal to four times the perimeter of a square. If a quarter of the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

A) 27/16 units B) 10.5 units
C) 9/4 units D) 27 units
 
Answer & Explanation Answer: A) 27/16 units

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Q:

A circle of diameter 26 cm having the two equal chords of length 10 cm is separated by a distance x cm. Calculate the distance x.

A) 20 B) 22
C) 24 D) 28
 
Answer & Explanation Answer: C) 24

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Q:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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Q:

If in-radius of an equilateral triangle is 3 cm. Calculate the perimeter (in m) of the equilateral triangle.

 

A) 6√3 B) 3√3
C) 12√3 D) 18√3
 
Answer & Explanation Answer: D) 18√3

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Q:

What is the equation of the line perpendicular to the line 2x + 3y= -6 and having Y-intercept 3?

A) 3x - 2y = 6 B) 3x - 2y = -6
C) 2x - 3y = -6 D) 2x - 3y = 6
 
Answer & Explanation Answer: B) 3x - 2y = -6

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Q:

Find the total surface area (in cm2) of a right circular cone of diameter 21 cm and slant height 11 cm.

A) 467.5 B) 384
C) 724 D) 709.5
 
Answer & Explanation Answer: D) 709.5

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