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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 corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?

A) a(√2 –1) B) a(√3 –1)
C) a/√2+2 D) a/3
 
Answer & Explanation Answer: A) a(√2 –1)

Explanation:

Since we are forming a regular octagon

so AE = AL = FB = BG and so on

So AE = SB = x/√2

AE + EF + FB = side of square = a (Given)

So x/√2 + x + x/√2 = a

X = a/(√2+1) = a(√2 -1)

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Q:

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is

A) 30 B) 90
C) 45 D) 60
 
Answer & Explanation Answer: D) 60

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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:

The curved surface area and the slant height of a right circular cone are 858 cm² and 13 cm respectively. Find its diameter (in cm).

 

A) 21 B) 42
C) 84 D) 63
 
Answer & Explanation Answer: B) 42

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Q:

Dodecahedron has 30 edges. How many vertices does it have?

A) 12 B) 16
C) 20 D) 10
 
Answer & Explanation Answer: C) 20

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Q:

In a triangle the length of the side opposite the angle which measures 30° is 9 cm, what is the length of the side opposite to the angle which measures 60°?

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

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Q:

Δ ABC is right angled at B. If m∠A = 30°. What is the length (in cm) of AB, if AC = 8 cm?

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

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Q:

A cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?

A) 7.15 cm B) 14.3 cm
C) 21.45 cm D) 28.6 cm
 
Answer & Explanation Answer: A) 7.15 cm

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