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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:

Calculate the value of ∡OBC + ∡BAC, if O is the circum-center of the triangle ABC inscribed in the circle.

 

 

 

A) 60 deg B) 90 deg
C) 120 deg D) 130 deg
 
Answer & Explanation Answer: B) 90 deg

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0 706
Q:

A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 5168.96 cubic cms B) 2584.48 cubic cms
C) 7753.44 cubic cms D) 1292.24 cubic cms
 
Answer & Explanation Answer: B) 2584.48 cubic cms

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0 704
Q:

If the in radius of the equilateral triangle is 8 cm then what is the value of circum radius (in cm) of the triangle?

A) 8 B) 16
C) 18 D) 20
 
Answer & Explanation Answer: B) 16

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0 703
Q:

A cylindrical vessel of height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

A) 8.2 cm B) 16.4 cm
C) 24.6 cm D) 32.8 cm
 
Answer & Explanation Answer: A) 8.2 cm

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0 701
Q:

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?

A) (0 , 13) B) (0, 5)
C) (0, -5) D) (0 , -13)
 
Answer & Explanation Answer: D) (0 , -13)

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0 699
Q:

The length of the diameter of the circle is 10 cm and length of the chord drawn in a circle is 6 cm. Find the distance (in cm) of chord from the center.

 

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

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0 693
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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0 692
Q:

In ΔPQR measure of angle Q is 90 deg. If tanP = 24/7, and PQ = 14cm, then what is the length (in cm) of side QR?

 

A) 50 B) 20
C) 26 D) 48
 
Answer & Explanation Answer: D) 48

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1 690