Given the volume of the cone below, identify the radius, height, and diameter.
Volume= 60π cubic centimeters

Question

Given the volume of the cone below, identify the radius, height, and diameter.
Volume= 60π cubic centimeters

anonymous · Answer

I will fan and medal!! PLEASE HELP!

anonymous · Answer

@matt101

matt101 · Answer

Do you know the equation for the volume of a cone?

anonymous · Answer

Not exactly, but the volume is given. I just have to find the radius, height, and diameter

matt101 · Answer

You need to know the equation for the volume, because volume is a function of radius and height. In other words, the equation will help you find the other variables. The volume of a cone is given by:

$$V = \pi r^2 {h \over 3}$$
Is there any other information provided about the cone? If not, we cannot solve this question, because otherwise there are an infinite number of combinations of r and h that would give 60π for your volume...

anonymous · Answer

Nothing else but multiple choice answers.

anonymous · Answer

18cm      5cm    6cm     4cm      9cm     12cm    10cm

matt101 · Answer

There really isn't anything you can do so I've googled your question and found a study guide from Edmentum that asks this exact question.

The truth is...it's a poor question! The solution they provide says that there are many different combinations of r and h that could give the volume in the question, just like I said. They get around it by saying BUT THERE'S ONLY ONE COMBINATION OF THE NUMBERS WE GAVE YOU THAT WORKS!

So basically you're expected to choose pairs of numbers from your answer choices and sub them into the volume equation for r and h to see if they work. Not much of a purpose to this question if you ask me...

Anyways, sorry about the rant - to solve this question, isolate hr^2 on one side of the volume equation, then factor the other side to its prime factors. This will let you easily see which number is being squared (that will be your r) and the leftover factor will be h. The diameter is just 2r.

anonymous · Answer

It's part of this "common core" junk. Obviously it's a poor question.. Common core is made to make no sense. Thanks for your help though!

matt101 · Answer

Haha sounds about right. Glad we could sort it out in the end!