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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 one side of a rhombus is 41 cm and its area is 720 sq.cm. What is the sum of the lengths of its diagonals?

A) 82 cm B) 90 cm
C) 98 cm D) 80 cm
 
Answer & Explanation Answer: C) 98 cm

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Q:

The curved surface area and the diameter of a right circular cylinder are 352 cm² and 14 cm respectively. Find its height (in cm).

A) 9 B) 8
C) 10 D) 11
 
Answer & Explanation Answer: B) 8

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Q:

If the side of the equilateral triangle is 8√3 cm, then what is the length (in cm) of the in radius of the triangle?

A) 2 B) 4
C) 8√3 D) 16√3
 
Answer & Explanation Answer: B) 4

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Q:

If the diameter of a circle is 35 cm, then what will be its circumference (in cm)?

A) 110 B) 220
C) 21 D) 42
 
Answer & Explanation Answer: A) 110

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Q:

In which of the following quadrilaterals opposite angles are supplementary?

A) Rhombus B) Parallelogram
C) Trapezium D) Cyclic quadrilateral
 
Answer & Explanation Answer: D) Cyclic quadrilateral

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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:

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

A) 10 units B) 8 units
C) 6 units D) 4 units
 
Answer & Explanation Answer: D) 4 units

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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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