Question

If h, C, V are respectively the height, the curved surface and the volume of a
cone, prove that 3ΠVh^3-C^2xh^2+9V^2

Answer 1

Step-by-step explanation:

Let r and l denote respectively the radius of the base and slant height of the cone.

l=

r

2

+h

2

V=

3

1

πr

2

h

C=πrl

Therefore,

3πVh

3

−C

2

h

2

+9V

2

=3π×

3

1

πr

2

h×h

3

−(πrl)

2

h

2

+9×(

3

1

πr

2

h)

2

=π

2

r

2

h

4

−π

2

r

2

l

2

h

2

+π

2

r

4

h

2

=π

2

r

2

h

4

−π

2

r

2

h

2

(r

2

+h

2

)+π

2

r

4

h

2

=π

2

r

2

h

4

−π

2

r

4

h

2

−π

2

r

2

h

4

+π

2

r

4

h

2

=0