Question

1. ice cream cone design

you are designing a new ice cream cone. the cone must hold 300 cubic centimeters of ice cream. if the height of the cone is 12 cm, what should the radius of the base be? use the volume formula ( v=\frac{1}{3}pi r^{2}h ) and provide your calculation and reasoning.

Explanation:

Step1: Substitute the values into the formula

Given \(V = 300\), \(h=12\), and the formula \(V=\frac{1}{3}\pi r^{2}h\). Substitute these values: \(300=\frac{1}{3}\times\pi\times r^{2}\times12\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation. \(\frac{1}{3}\times12 = 4\), so the equation becomes \(300 = 4\pi r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation by \(4\pi\). \(r^{2}=\frac{300}{4\pi}=\frac{75}{\pi}\).

Step4: Solve for \(r\)

Take the square root of both sides. \(r=\sqrt{\frac{75}{\pi}}\approx\sqrt{\frac{75}{3.14}}\approx\sqrt{23.89}\approx4.89\) (rounded to two decimal places).

Answer:

The radius of the ice - cream cone is approximately \(4.89\) cm.