Sphere , Hemisphere , prism and pyramid important arithmetic formulae | mensuration short tricks.

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Today we are going to talk about some important arithmetic formulae on sphere , hemisphere , prism and pyramid.

Students are advised to learn all these formulae and keep practicing with it.
SOME IMPORTANT SUTRAS

*SPHERE
1). Volume of solid sphere = (4/3).πr^3= πd^3/6
2). Total surface area of solid sphere = 4πr^2 = πd^2
3). Volume of hollow sphere = (4/3).π(R^3-r^3)
4). Total surface area of hollow sphere =
4π(R^2-r^2)
5). Radius of sphere = (3V/4π)^1/3
6). Diameter of sphere = (6V/π)^1/3
7). Radius of sphere = √TSA/4π
8). Diameter of sphere = √TSA/π
9). t is the thickness of the material of the hollow sphere , if R is larger radius then smaller radius is= R-t
10). Volume of capsule = π r^2.[(4r/3)+h]
11). Total surface area of capsule =  2πr.(2r+h)
12). Volume of sphere = (r/3). surface area
13). Surface area of sphere = 3V/r
14). Radius of largest sphere in cube = a/2
15). Volume of largest sphere in cube = πa^3/6 =
11a^3/21
16). Surface area of largest sphere in cube =πa^2
17). Side of largest cube in sphere = d/√3 = 2r/√3
18). Volume of largest cube in sphere =8r^3√3/9
19). Volume of parts of the Sphere with cube =
(3π-2√3).d^3/18
20). Surface area of largest cube in sphere =2d^2
= 8r^2
* HEMISPHERE
1). Total surface area of solid hemisphere =3πr^2
2).Total Curved surface (inner and outer) area of hollow hemisphere = 2π(r1^2+r2^2)
3). Surface area of the circular strip of thickness t, (R-r) of hollow hemisphere = π(R^2-r^2)
4). Volume of solid hemisphere = (2/3).πr^3
5). Volume of hollow hemisphere =
(2/3)π(R^3-r^3)
6). The radius of the sphere of the maximum volume, which is cut from the hemisphere of radius r is = r/2
* PRISM
1). Volume of prism = base area ×h = A×h
2). Surface area of prism = perimeter of base×h
3). Total surface area of prism = 2A+ph
* PYRAMID
1). Volume of the pyramid = Base area×h/3= Ah/3
2). Surface area of pyramid = n.a.l/2
(Where , n is no. of faces , a is base side , l is slant height)
3). Total surface area of the pyramid = A+(n.a.l/2)
4). Slant height of Pyramid = √(h^2+r^2)