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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:

If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, find its total surface area.

A) 27720 sq cm B) 4620 sq cm
C) 6930 sq cm D) 13860 sq cm
 
Answer & Explanation Answer: D) 13860 sq cm

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Q:

If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm and its area is 54 cm². Find the distance between its parallel sides (in cm).

A) 6 B) 3
C) 12 D) 9
 
Answer & Explanation Answer: A) 6

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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:2 and area of ΔABC is 45 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A) 20 B) 40
C) 15 D) 30
 
Answer & Explanation Answer: B) 40

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0 1133
Q:

ΔABC is similar to ΔDEF. Length of AB is 18 cm and length of the corresponding side DE is 10 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

A) 5:9 B) 9:5
C) 81:25 D) 25:81
 
Answer & Explanation Answer: B) 9:5

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0 1129
Q:

What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

A) 2 B) 4
C) 3 D) 6
 
Answer & Explanation Answer: B) 4

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0 1127
Q:

What is the diameter (in cm) of a sphere of surface area 6.16 sq cm?

A) 1.4 B) 0.7
C) 2.8 D) 2.1
 
Answer & Explanation Answer: A) 1.4

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0 1123
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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0 1123
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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