Important Mensuration formulas and short notes for 3D figures

Given is the cuboid of lenth l, breadth b and height h. 

T.S.A. = 2(lb + bh + lh)

Volume = lbh

Diagonal =  

Important:  If area of faces of cuboid are x,y and z

Then, volume of cuboid 

#Cube

Let the side of given cube is 'a'.

T.S.A. = 6a²

Volume = a³

Diagonal of cube =  

# Sphere

let the radius of given sphere is 'r' and in case of sphere total surface area is equal to curved surface area.

C.S.A. = T.S.A. = 

Volume =  

# Hemi-Sphere

Assume r is the radius of given hemisphere.

# Quarter-Sphere

Let 'r' is the radius of given diagram. You have to imagine this diagram, this is 1/4^th part of Sphere.

# Cylinder

# Hollow-Cylinder

r₁ = outer radius

r₂ = inner radius

# Frustum

# Cone

r = radius

h = height of cone

l = slant height

# Important relation between radius, height and slant height of similar cone.

Important:
1.From a solid cylinder no. of maximum solid cone of same height and radius as cylider are 3.
2.From a solid sphere, no. of maximum solid cone having height and radius equal can be made are 4.
3.From a solid hemisphere, no. of maximum solid cone having height and radius equal can be made are 2.