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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:

Radius of cross section of a solid right circular cylindrical rod is 3.2 dm. The rod is melted and 44 equal solid cubes of side 8 cm are formed. The length of the rod is (Take Π = 22/7)

A) 56 cm B) 7 cm
C) 5.6 cm D) 0.7 cm
 
Answer & Explanation Answer: B) 7 cm

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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:

ABC is a right angled triangle with angle A = 90 deg. Then the value of cos2A+cos2B+cos2C is

A) 2 B) 1
C) 0 D) 3
 
Answer & Explanation Answer: B) 1

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Q:

The point where the 3 medians of a triangle meet is called

A) centroid B) Incentre
C) Circumcentre D) orthocentre
 
Answer & Explanation Answer: A) centroid

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Q:

In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?

A) 13 B) 26
C) 39 D) 52
 
Answer & Explanation Answer: A) 13

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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:

The length, breadth and height of a cuboid are 12 cm, 8 cm and 6 cm respectively. The volume of the cuboid is (Use π = 22/7)

A) 1152 cubic cms B) 288 cubic cms
C) 576 cubic cms D) 864 cubic cms
 
Answer & Explanation Answer: C) 576 cubic cms

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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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