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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 area of a semicircle is 1925 cm2. Calculate its perimeter (in cm).

A) 360 B) 80
C) 160 D) 180
 
Answer & Explanation Answer: D) 180

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Q:

Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is

A) 7.5 cm B) 9 cm
C) 8 cm D) 10 cm
 
Answer & Explanation Answer: B) 9 cm

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Q:

Find the curved surface area (in cm2) of a hemisphere of diameter 7 cm.

A) 88 B) 55
C) 77 D) 66
 
Answer & Explanation Answer: C) 77

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Q:

If ABCD is a trapezium, AC and BD are the diagonals intersecting each other at point O. Then AC : BD is

A) AB + AD : DC + BC B) AO - OC : OB - OD
C) AB : CD D) AD : BC
 
Answer & Explanation Answer: B) AO - OC : OB - OD

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Q:

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

A) 100 B) 400
C) 200 D) 150
 
Answer & Explanation Answer: A) 100

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Q:

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area (in sq cm) of the circle?

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

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Q:

O is the centre of a circle and AB is the tangent to it touching at B . If OB = 3 cm. and OA = 5 cm , then the measure of AB in cm

A) √34 B) 2
C) 8 D) 4
 
Answer & Explanation Answer: D) 4

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Q:

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A) 240 B) 120
C) 210 D) 420
 
Answer & Explanation Answer: D) 420

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