Question

An ice cream cone is filled with a vanilla and chocolate ice cream at a ratio of 2:

1 if the diameter of the cone is 2 inches and the height is 6 inches approximately what is the volume of vanilla ice cream in the cone

Answer 1

`\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ----------\\ diameter=2\\ r=(diameter)/(2)\\ \quad = 1\\ h=6 \end{cases}\implies V=\cfrac{\pi\cdot 1^2\cdot 6}{3} \\\\\\ V=2\pi \\\\ -------------------------------`


`\bf \cfrac{\stackrel{vanilla}{volume}}{\stackrel{chocolate}{volume}}\qquad 2:1\qquad \cfrac{2}{1}\implies \cfrac{2\cdot (V)/(2+1)}{1\cdot (V)/(2+1)}\implies \cfrac{2\cdot (2\pi )/(2+1)}{1\cdot (2\pi )/(2+1)} \\\\\\ \cfrac{2\cdot (2\pi )/(3)}{1\cdot (2\pi )/(3)}\implies \cfrac{\quad (4\pi )/(3)\quad }{(2\pi )/(3)}`

Answer 2

Answer: Volume of vanilla ice cream in the cone=
`(4\pi)/(3)\ in^3`

Explanation:

Given : The diameter of cone = : d= 2 inches

Then radius of cone = Half of diameter = 1 inch

Height of cone = 6 inches.

Volume of cone =
`(1)/(3)\pi r^2 h` , where r= radius , h= height of cone.

Then, Volume of cone =
`(1)/(3)\pi (1)^2 (6)=(1)/(3)\pi (6)= 2 \pi\ in^3`

Since ice cream cone is filled with a vanilla and chocolate ice cream at a ratio of 2:

1.

Let x be the volume of chocolate ice cream , then the volume of vanilla ice-cream will be 2x.

Also, Volume of cone=Volume of vanilla ice cream + Volume of chocolate ice cream

i.e.
`2\pi = 2x+x\\\\ \Rightarrow\ 3x= 2\pi \\\\\Rightarrow\ x=(2\pi)/(3)\ in^3`

Then , the volume of vanilla ice cream in the cone=
`2x=(4\pi)/(3)\ in^3`