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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 length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

A) 7/2 B) 7
C) 7√2 D) 14
 
Answer & Explanation Answer: B) 7

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Q:

In the given figure, PQ is the diameter of the circle. What is the measure (in degrees) of QSR?

A) 23 B) 37
C) 47 D) 57
 
Answer & Explanation Answer: C) 47

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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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Q:

In an isosceles triangle ABC, AB = AC, XY || BC. If ∡A = 30, then ∡BXY = 

A) 75° B) 30°
C) 150° D) 105°
 
Answer & Explanation Answer: D) 105°

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Q:

Which of the following is not true for a rhombus?

A) All sides are congruent B) Opposite sides are parallel
C) Diagonals are equal D) Diagonals bisect each other at right angles
 
Answer & Explanation Answer: C) Diagonals are equal

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Q:

A cone of radius 3.5 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 7 cm. What will be the height of water in this vessel?

A) 2 cm B) 0.33 cm
C) 0.5 cm D) 1 cm
 
Answer & Explanation Answer: D) 1 cm

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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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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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