Question

at ericas ice cream shop, customers can choose from several different types of cones for their ice cream. the table below shows the dimensions of each type of cone. order the volumes of the ice cream cones from least to greatest. what is the mean volume of the ice cream cones given in the table? round your answer to the nearest whole number. cubic centimeters

Explanation:

Step1: Calculate the volume of each cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\).

• For the waffle cone: \(r = 4.2\) cm, \(h=13\) cm.

\(V_{waffle}=\frac{1}{3}\times\pi\times(4.2)^{2}\times13=\frac{1}{3}\times\pi\times17.64\times13\approx241.27\) \(cm^{3}\)

• For the sugar cone: \(r = 4.5\) cm, \(h = 12\) cm.

\(V_{sugar}=\frac{1}{3}\times\pi\times(4.5)^{2}\times12=\frac{1}{3}\times\pi\times20.25\times12 = 254.47\) \(cm^{3}\)

• For the mini cone: \(r=2.5\) cm, \(h = 9\) cm.

\(V_{mini}=\frac{1}{3}\times\pi\times(2.5)^{2}\times9=\frac{1}{3}\times\pi\times6.25\times9= 58.90\) \(cm^{3}\)

• For the pretzel cone: \(r = 3.9\) cm, \(h=10\) cm.

\(V_{pretzel}=\frac{1}{3}\times\pi\times(3.9)^{2}\times10=\frac{1}{3}\times\pi\times15.21\times10\approx159.19\) \(cm^{3}\)

Step2: Order the volumes

Comparing the volumes: \(V_{mini}(58.90)<V_{pretzel}(159.19)<V_{waffle}(241.27)<V_{sugar}(254.47)\)

Step3: Calculate the mean volume

The mean formula is \(\bar{V}=\frac{V_{1}+V_{2}+V_{3}+V_{4}}{4}\)
\(\bar{V}=\frac{58.90 + 159.19+241.27+254.47}{4}=\frac{713.83}{4}=178.46\approx178\) \(cm^{3}\)

Answer:

Order from least to greatest: mini cone, pretzel cone, waffle cone, sugar cone.
Mean volume: \(178\) cubic centimeters.