Question

The diameter and volume of a sphere and a cone are equal. Find the ratio of height and

diameter of the cone.​

Answer 1

Step-by-step explanation:

Let r be the common radius. Then,

h= height of the cone = height of the cylinder =2r

∴V

1

= Volume of the sphere =

3

4

πr

3

V

2

= Volume of the cylinder =πr

2

h=πr

2

×2r=2πr

3

V

3

= Volume of the cone =

3

1

πr

2

h =

3

1

πr

2

×2r=

3

2

πr

3

⇒V

1

:V

2

:V

3

=

3

4

:2:

3

2

=2:3:1

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