Surface Areas And Volumes

Formulae

Cuboid:

* If l, b, h are respectively the length, breadth and height of a cuboid then,

1. LSA (or) Area of four walls = 2h (l + b)

2. TSA = 2 (lb + bh + lh)

3. V = lbh

4. Sum of all the edges = 4 (l + b + h)

5. diagonal (D) = √(l² + b² + h²)

Cube:

* If 'a' is the edge of a cube then,

1. LSA (or) Area of four walls = 4a²

2. TSA = 6a²

3. Volume (v) = a³

4. sum of all the edges = 12a

5. Diagonal (d) = √3a (or) a√3

Cylinder:

* If h, r are respectively the height (vertical) and radius of a cylinder then,

1. CSA = 2πrh

2. TSA = 2πr (h + r)

3. Volume (V) = π r² h

4. Area of each base = π r² (circle area)

Hollow Cylinder :

* If R, r are respectively the outer and inner radii, 'w' the width 'h' the height

 of a hollow cylinder then,

1. CSA = 2 π h (R + r)

2. TSA = 2 π (R + r) (h + R - r)

3. Volume (V) = π h (R² - r²)

4. Area of each base = π (R² - r²)

5. Width (w) = R – r

Cone

* If r, h, l are respectively the radius, height (vertical) and slant height of a

 cone then,

1. CSA = π r l

2. TSA = π r (l + r)

3. Volume (V) = 1/3 π r² h

* Volume of cone = 1/3 volume of cylinder

 (Volume of Cone)/(Volume of Cylinder )= 1/3

4. Area of the base = π r²

5. Slant height (l) = √(h² + r²) ̅

      r = √(l² - h²) ̅

      h = √(l² - r²) ̅

Sphere

* If 'r' being the radius of a sphere, then,

1. CSA (or) Surface area (or) TSA (or) area = 4 π r²

2. Volume = 4/3 π r³

Hemi - Sphere

* If 'r' being the radius of a hemisphere, then

1. CSA = 2π r²

2. TSA = 3π r²

3. Volume (V) = 2/3 π r³

4. Area of the base = π r²

Hollow Sphere

* If R, r are respectively the outer and inner radii of a hollow sphere then

1. Volume (V) = 4/3 π (R³ - r³)

2. Outer area = 4 π R²

3. Inner area = 4 π r²