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Important Mensuration formulas and short notes for 3D figures

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

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 1/4th 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.
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