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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 spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold.

 

A) 4929 cub.cm B) 4939 cub.cm
C) 4932 cub.cm D) 4930 cub.cm
 
Answer & Explanation Answer: B) 4939 cub.cm

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Q:

In the two triangles ABC and DEF the sides AB = DE and BC = EF. Which of the following option is correct which results in the ∆ABC ≅∆DEF?

 

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

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Q:

The total surface area of a cube is 181.5 cm². Find its side (in cm).

A) 6.5 B) 4.5
C) 7.5 D) 5.5
 
Answer & Explanation Answer: D) 5.5

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Q:

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Then the number of sides of each polygon are

A) 10, 20 B) 4, 8
C) 3, 6 D) 5, 10
 
Answer & Explanation Answer: D) 5, 10

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Q:

What is the sum of the measures of all the interior angles of a regular polygon of 5 sides?

A) 720 B) 1080
C) 1260 D) 540
 
Answer & Explanation Answer: D) 540

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Q:

The lengths of the two diagonals of a rhombus are 6 cm and 8 cm. Find the length of its perimeter (in cm).

A) 20 B) 10
C) 40 D) 30
 
Answer & Explanation Answer: A) 20

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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:

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of remaining solid?

A) 272 cub.cm B) 270 cub.cm
C) 300 cub.cm D) 277 cub.cm
 
Answer & Explanation Answer: D) 277 cub.cm

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