Question

The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is

Options

• \[3 \pi r^2\]

• `1/3pir^3`

   

• \[\frac{\pi r^2}{3}\]

• \[3 \pi r^3\]

Answer 1

Radius of hemisphere = r

Therefore,

The radius of cone = r

and height h = r

Then,

Volume of cone

`=1/3 pir^2 h `

`=1/3pir^2 xx r`

`=1/3 pir^3 ("unit")^3`