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 Volume and Surface Area Questions

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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:

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

A) 493 B) 7
C) 14 D) 983
 
Answer & Explanation Answer: B) 7

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Q:

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?

A) 12 B) 14
C) 16 D) 28
 
Answer & Explanation Answer: D) 28

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Q:

A right circular cylinder has height as 18 cm and radius as 7 cm. The cylinder is cut in three equal parts (by 2 cuts parallel to base). What is the percentage increase in total surface area?

A) 62 B) 56
C) 48 D) 52
 
Answer & Explanation Answer: B) 56

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Q:

Find the circumference (in cm) of a circle of radius 17.5 cm.

A) 140 B) 110
C) 38 D) 76
 
Answer & Explanation Answer: B) 110

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Q:

ABCD is a trapezium in which AB is parallel to CD and AB = 4(CD). The diagonals of the trapezium intersects at O. What is the ratio of area of triangle DCO to the area of the triangle ABO?

A) 1 : 4 B) 1 : 2
C) 1 : 8 D) 1 : 16
 
Answer & Explanation Answer: D) 1 : 16

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Q:

If PA and PB are tangents to the circle with centre O such that ∠APB=50°, then the ∠OAB=

A) 25° B) 30°
C) 40° D) 50°
 
Answer & Explanation Answer: A) 25°

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Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the difference between perimeter of triangle ABC and perimeter of triangle ADC?

A) 4 cm B) 5 cm
C) 6 cm D) 7 cm
 
Answer & Explanation Answer: C) 6 cm

Explanation:
Perimeter of triangle ABC – Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm
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Q:

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

A) 8cm B) 6cm
C) 4cm D) 12cm
 
Answer & Explanation Answer: B) 6cm

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