A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

acannell · Answer

Let's hope for your sake, in 30 years or so, you can say the same. 

This isn't pre-algebra, it's geometry. It's also easy. 

You already know the area of a circle: pi * r-squared (we'll show that as r^2 here) 

Volume is area times height. So the cylinder's volume will be: 
pi * r^2 * h (height) 

becomes 
3.14 * 4^2 * 5 

3.14 x 16 x 5 = volume of cylinder. 

The formula for a cone is the same, divided by 3. The volume of a cone is area of its base, times height, divided by three. Dividing by three makes the formula account for the fact that the volume the cone fills decreases as it gets closer to its peak. It doesn't matter how wide or narrow a cone it is. So the formula looks like this: 

(pi * r^2 * h) / 3 

becomes 

(3.14 * 4^2 * 15) / 3 

Since the formula is that a cone will have 1/3 the volume of a cylinder whose base and height are otherwise the same, but in this case we have a cone that is 3 times as high, the enclosed volumes are the same.

acannell · Answer

Hope i helped!!!

christiannewsom · Answer

lol lets hope for my sake

acannell · Answer

XD

christiannewsom · Answer

thats the last one for right now

acannell · Answer

Okay. Let me know if you need help!! :)