Question

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

Answer 1

Answer: Volume of vanilla ice cream in the cone= $\dfrac{4\pi}{3}\ in^3$

Step-by-step 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 = $\dfrac{1}{3}\pi r^2 h$ , where r= radius , h= height of cone.

Then, Volume of cone = $\dfrac{1}{3}\pi (1)^2 (6)=\dfrac{1}{3}\pi (6)= 2 \pi\ in^3$

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. $2\pi = 2x+x\\\\ \Rightarrow\ 3x= 2\pi \\\\\Rightarrow\ x=\dfrac{2\pi}{3}\ in^3$

Then , the volume of vanilla ice cream in the cone= $2x=\dfrac{4\pi}{3}\ in^3$

Answer 2

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

$\bf \cfrac{\stackrel{vanilla}{volume}}{\stackrel{chocolate}{volume}}\qquad 2:1\qquad \cfrac{2}{1}\implies \cfrac{2\cdot \frac{V}{2+1}}{1\cdot \frac{V}{2+1}}\implies \cfrac{2\cdot \frac{2\pi }{2+1}}{1\cdot \frac{2\pi }{2+1}} \\\\\\ \cfrac{2\cdot \frac{2\pi }{3}}{1\cdot \frac{2\pi }{3}}\implies \cfrac{\quad \frac{4\pi }{3}\quad }{\frac{2\pi }{3}}$