# Study Notes on Mensuration (3D)

By Gaurav Mohanty|Updated : January 3rd, 2022

We have already discussed Mensuration 2D Short notes, here we will discuss all Mensuration 3D figures. You can also know some important facts about 3D figures. In this article, abbreviations used are TSA = Total Surface Area, CSA = Curved Surface Area.

## 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 1/4th part of Sphere.

## Cone

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.