Question

If h, c, V are respectively the height, the curved surface and the volume of a cone, prove that 3Vh3 -c 2h 2+9V2 .​

Answer 1

Answer:

Step-by-step explanation:

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

I=√r2+h2

V=1/3πr2h

C=πrl

Therefore,

3πVh

−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

Answer =0