Question

Question #df371

Answer 1

`a)` `11.5` `"in"^3`

Explanation:

I think your cone looks like this

We need to find the approximation of ice cream that can be filled in this

For that, we can subtract the total volume of the cone with the volume of the spherical bubble gum

We need to find the volume of the cone and the spherical bubble gum

We use,

`color(orange)("Volume of cone"=1/3pir^2h`

`color(violet)("Volume of sphere"=4/3pir^3`

Where,

`color(red)(r="radius"`

`color(red)(h="height"`

`color(red)(pi=22/7=3.14`

Lets solve it

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(orange)("Volume of cone"=1/3pir^2h`

`rarrcolor(orange)(1/3*22/7*1.75^2*3.5` `color(orange)("in"^3`

`rarrcolor(orange)(22/21*3.0625*3.5` `color(orange)("in"^3`

`rarrcolor(orange)(22/21*10.71` `color(orange)("in"^3`

`rarrcolor(orange)(1.047*10.71` `color(orange)("in"^3`

`rarr~~color(green)(11.21` `color(green)("in"^3`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(violet)("Volume of sphere"=4/3pir^3` `color(violet)("in"^3`

`rarrcolor(violet)(4/3*22/7*0.5^3` `color(violet)("in"^3`

`rarrcolor(violet)(1.333*3.14*0.12` `color(violet)("in"^3`

`rarrcolor(violet)(4.185*0.12` `color(violet)("in"^3`

`rarr~~color(green)(0.5` `color(green)("in"^3`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtract the volumes

`color(purple)(11.21 -0.5=11.16` `color(purple)("in"^3`

The closest approximation of `color(purple)(11.16` in the options is `color(green)(11.15`