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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 a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are

A) 15, 130 B) 15, 125
C) 35, 40 D) 30, 150
 
Answer & Explanation Answer: B) 15, 125

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Q:

A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

A) 26.46 cm B) 39.69 cm
C) 13.23 cm D) 52.92 cm
 
Answer & Explanation Answer: C) 13.23 cm

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Q:

The base and hypotenuse of a right angled triangle is 12 cm and 5 cm respectively. Find the circum-radius (in cm) of the triangle.

 

A) 5 B) 6
C) 6.5 D) 7
 
Answer & Explanation Answer: C) 6.5

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Q:

ΔABC is right angled at B. BD is the altitude. AD is 8 cm and DC is 50 cm. What is the length of BD?

A) 25 cm B) 20 cm
C) 16 cm D) 15 cm
 
Answer & Explanation Answer: B) 20 cm

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Q:

An angle is greater than its complementary angle by 40°. Find the measure of the angle?

A) 25° B) 65°
C) 130° D) 50°
 
Answer & Explanation Answer: B) 65°

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Q:

The lengths of the two diagonals of a rhombus are 7 cm and 24 cm. Find the length of its perimeter (in cm).

A) 25 B) 100
C) 75 D) 50
 
Answer & Explanation Answer: D) 50

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Q:

Find the volume (in cm3) of a right circular cylinder of diameter 42 cm and height 14 cm.

A) 19404 B) 18018
C) 17321 D) 16729
 
Answer & Explanation Answer: A) 19404

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Q:

If the lengths of the two parallel sides of a trapezium are 7 cm and 9 cm and its area is 80 cm2. Find the distance between its parallel sides (in cm).

A) 5 B) 10
C) 20 D) 15
 
Answer & Explanation Answer: B) 10

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