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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 diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 49π sq cm?

A) 196 sq cm B) 154 sq cm
C) 124 sq cm D) 98 sq cm
 
Answer & Explanation Answer: A) 196 sq cm

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Q:

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A) 24 B) 20
C) 27 D) 28
 
Answer & Explanation Answer: A) 24

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0 1152
Q:

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

A) 247200 B) 269500
C) 312500 D) 341800
 
Answer & Explanation Answer: B) 269500

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0 1150
Q:

If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is

A) 60 cm2 B) 32.5 cm2
C) 65 cm2 D) 30 cm2
 
Answer & Explanation Answer: A) 60 cm2

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Q:

Length of the sides of a triangle are a, b, c respectively. If a2 + b2 + c2 = ab +bc + ca then the triangle is

A) isosceles B) equilateral
C) scalene D) right­-angled
 
Answer & Explanation Answer: B) equilateral

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0 1147
Q:

The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2 . What is the radius (in cm) of the larger circle?

A) 56 B) 42
C) 63 D) 49
 
Answer & Explanation Answer: D) 49

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Q:

The radius of a hemisphere is 7 cm, find its volume?

A) 718.67 cubic cm B) 1437.34 cubic cm
C) 239.56 cubic cm D) 359.34 cubic cm
 
Answer & Explanation Answer: A) 718.67 cubic cm

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0 1141
Q:

The length of the diagonal and the breadth of a rectangle are 17 cm and 8 cm respectively. Find its perimeter (in cm).

A) 92 B) 46
C) 42 D) 84
 
Answer & Explanation Answer: B) 46

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