Question

What is the volume of the item described? An ice cream cone with a cone of radius 2 cm and height of 9 cm with a hemisphere of ice cream on top of radius 2 cm. Select the exact answer in terms of ​ π ​ and the approximate answer rounded to the nearest whole number

Answer 1

The volume of item is
`(52)/(3)\pi`.

Explanation:

The volume of cone

`V_1=(1)/(3)\pi r^2h`

Where r is radius of cone and h is the height of cone.

It is given that the radius of cone is 2 cm and the height of cone is 9 cm. So, the volume of cone is

`V_1=(1)/(3)\pi (2)^2(9)=12\pi`

The volume of hemisphere

`V_2=(2)/(3)\pi r^3`

Where r is radius of hemisphere.

It is given that the radius of hemisphere is 2 cm. So, the volume of hemisphere is

`V_2=(2)/(3)\pi (2)^3=(16)/(3)\pi`

The volume of ice cream is

`V=V_1+V_2`

`V=12\pi+(16)/(3)\pi`

`V=(36+16)/(3)\pi`

`V=(52)/(3)\pi`

Therefore the volume of item is
`(52)/(3)\pi`.

Answer 2

Volume of hemisphere = 2πr³/3
Volume of cone = πr²h/3

Where r = 2 and h = 9

Volume = volume of hemisphere + volume of cone
Volume = 2π(2)³/3 + π(2)²(9)/3
Volume = 16π/3 + 36π/3
Volume = 52π/3