VOLUME AND SURFACE AREA -> IMPORTANT FACTS AND FORMULAE

I. CUBIOD 
Let length = l, breadth = b and height = h units. Then, 

1. Volume = (l x b x h) cubic units. 

2. Surface area = 2 (lb + bh + lh) 

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 = √3 a units. 

III. CYLINDER 
Let radius of base = r and Height (or length) = h Then, 

1. Volume = (∏r²h) cubic units.

 2. Curved surface area = (2∏rh) sq. units.

3. Total surface area = (2∏rh + 2∏r² sq. units) = 2∏r (h + r) sq. units. 

IV. CONE
Let radius of base = r and Height = h. Then, 

1. Slant height, l = √h² + r ² units. 

2. Volume = [1/3 ∏r²h] cubic units. 

3. Total surface area = (∏rl + ∏r²) sq.units. 


V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume = [4/3 ∏r3] cubic units. 

2. Surface area = (4∏r²) sq. units. 

VI. HEMISPHERE 
Let the radius of a hemisphere be r. Then, 

1. Volume = [2/3 ∏r3] cubic units. 

2. Curved surface area = (3∏r²) sq. units. 

3. Total surface area = (3∏r²) sq. units. Remember : 1 litre = 1000 cm³.