Question

A solid is in the form of a cone of vertical height h mounted on the top base of a right circular cylinder of height 1/3 h. The circumference of the base of the cone and that of the cylinder are both equal to C. If V be the volume of the solid, prove that
C = 4√(ЗπV/7h)​

Answer 1

Answer:

The volume of the cone is given by, V

cone

=

3

1

πr

2

h, where 'r' is the base radius of the cylinder and cone.

The volume of the cone is given by, V

cyl

=

3

1

πr

2

h

The circumference of the base is given by, C=2πr or r=

2π

C

The total volume of the solid is V=

3

1

πr

2

h+

3

1

πr

2

h=

3

2

πr

2

h

Substituting for r in V,

V=

3

2

π(

2π

C

)

2

h

⇒V=

3

2

πh×

4π

2

C

2

⇒V=

6π

C

2

h

⇒C=

h

6πV

.