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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:

The volume of a right circular cone, whose radius of the base is same as its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is

 

A) 33 : 23 B) 2 : 1
C) 1 : 1 D) 43 : 1
 
Answer & Explanation Answer: D) 43 : 1

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Q:

In ΔABC, the medians AD and BE meet at G. The ratio of the areas of ΔBDG and the quadrilateral GDCE is

A) 1 : 2 B) 1 : 3
C) 2 : 3 D) 3 : 4
 
Answer & Explanation Answer: A) 1 : 2

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Q:

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A) 31276 B) 36194
C) 25182 D) 33264
 
Answer & Explanation Answer: D) 33264

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Q:

If an interior of a regular polygon is 170o, then the number of sides of the polygon is

A) 30 B) 20
C) 18 D) 27
 
Answer & Explanation Answer: A) 30

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Q:

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A) 240 B) 120
C) 210 D) 420
 
Answer & Explanation Answer: D) 420

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Q:

If the side AB of an equilateral triangle ABC is equal to 12 cm. Calculate the length( in cm) of the AO, if O is the centroid of the triangle.

A) 2√3 B) 3√3
C) 4√3 D) 9√3
 
Answer & Explanation Answer: C) 4√3

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Q:

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

A) 30° B) 45°
C) 60° D) 75°
 
Answer & Explanation Answer: A) 30°

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Q:

Curved surface area of a cylinder is 660 sq cm. If circumference of its base is 44 cm, find the volume of the cylinder?

A) 4620 cubic cm B) 2310 cubic cm
C) 6930 cubic cm D) 1155 cubic cm
 
Answer & Explanation Answer: B) 2310 cubic cm

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