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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:

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 50°, then what is the value (in degrees) of ∠PBC?

A) 30 B) 45
C) 50 D) 60
 
Answer & Explanation Answer: C) 50

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Q:

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3 B)  6√3
C) 6 D) 3
 
Answer & Explanation Answer: A) 3√3

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Q:

In a triangle ABC, if ∡A +∡C = 140° and ∡A + 3∡B = 180°, then ∡A is equal to

A) 80° B) 40°
C) 60° D) 20°
 
Answer & Explanation Answer: C) 60°

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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:

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is

A) 31.5 units B) 36 units
C) 27 units D) 18 units
 
Answer & Explanation Answer: B) 36 units

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Q:

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm B) 10cm
C) 12cm D) 8cm
 
Answer & Explanation Answer: C) 12cm

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Q:

If ABCD is a Cyclic Quadrilateral, then the value of Cos2A - Cos2B - Cos2C + Cos2D is

 

 

A) -1 B) 2
C) 1 D) 0
 
Answer & Explanation Answer: C) 1

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Q:

The surface area of a sphere is 5544 cm2. Find its diameter (in cm).

A) 42 B) 21
C) 84 D) 63
 
Answer & Explanation Answer: A) 42

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