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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)

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