Study Notes on Mensuration (3D)

Cuboid :

Given is the cuboid of length 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, the volume of a cuboid 

Cube

Let the side of the given cube is 'a'.

T.S.A. = 6a²

Volume = a³

Diagonal of cube =  

Sphere

let the radius of the given sphere is 'r' and in the case of sphere total surface area is equal to the 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 the 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 the maximum solid cone of same height and radius as cylinder are 3.
2. From a solid sphere, no. of a maximum solid cone having height and radius equal can be made are 4.
3. From a solid hemisphere, no. of a maximum solid cone having height and radius equal can be made are 2.