Discovering the Formula for Volume of a Sphere

Discovering the Formula for Volume of a Sphere

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Recall Volume of a Cylinder

r2π

V = x Heightπr2



r2π

hV = πr2 h



r2π

hV = πr2h

3


r2π

hV = πr2h

3

Recall Volume of a Cone


r2π


+ =h


r2π


+ = h


r2π


+ =r


r2π


+ = r


r2ππr2h

3


+ =πr2h

3+ = Volume of

a Sphere


r2ππr2h

3


+ = hr

πr2h3

+ = Volume of a Sphere

r


r2ππr2h

3

+ = hr

πr2h3


r

r

r


r2ππr h

3

+ =πr h

3+ = Volume of

a Sphere

r

r

r

rh

r

r

r

r


r2ππr h

3

+ =πr h

3+ = Volume of

a Sphere

r

r

r

rh

r r r r( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

r r r r( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

rr rr( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

( )2r ( )2rr r

rπrπ


r2ππr3

+ =πr3


r

r

r

rh

2 2r r

rπrπ


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2r r

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2( )

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

22( )

4 r3πr3π


r2π3

+ =

3= Volume of

a Sphere

r

r

r

rh

( )

4 r3πr3π


r2π3

+ =

3= Volume of

a Sphere

r

r

r

rh

4 r3πr3π


r2π33=V

Volume of a Sphere

4 r3πr3π


r2π33=V or 4 r3πr3π

33

Volume of a Sphere

=V

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