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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 radius of the circle circumscribing the three vertices of an equilateral triangle is 12 cm. Determine the height (in cm) of the equilateral triangle

A) 12 B) 14
C) 18 D) 20
 
Answer & Explanation Answer: C) 18

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4 1600
Q:

The total surface area of a hemisphere is 166.32 sq cm, find its radius?

A) 4.2 cm B) 8.4 cm
C) 1.4 cm D) 2.1 cm
 
Answer & Explanation Answer: A) 4.2 cm

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0 1598
Q:

At least one diagonal bisects the other in a _____.

A) Trapezium B) Isosceles trapezium
C) Kite D) Cyclic quadrilateral
 
Answer & Explanation Answer: C) Kite

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1 1597
Q:

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is

A) 3:1 B) 1:3
C) 7:3 D) 3:7
 
Answer & Explanation Answer: C) 7:3

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0 1597
Q:

A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are

A) 6 cm and 12 cm B) 4 cm and 8 cm
C) 3 cm and 6 cm D) 2 cm and 4 cm
 
Answer & Explanation Answer: C) 3 cm and 6 cm

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0 1597
Q:

The length, breadth and height of a cuboid are in the ratio 19 : 11 : 13. If length is 30 cm more than height, then what is the volume (in cub.cm) of this cuboid?

A) 81510 B) 89665
C) 195300 D) 339625
 
Answer & Explanation Answer: D) 339625

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0 1595
Q:

AB is a chord of the circle and its center is “O”. ON is perpendicular to AB. If the length of AB=20 cm, ON-(2√11) cm, find the radius (in cm) of the circle.

A) 10 B) 12
C) 13 D) 15
 
Answer & Explanation Answer: B) 12

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0 1588
Q:

The total surface area of a hemisphere is 462 sq cm, what is its curved surface area? (Take π = 22/7)

A) 616 sq cms B) 154 sq cms
C) 308 sq cms D) 462 sq cms
 
Answer & Explanation Answer: C) 308 sq cms

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0 1583