Please help, what effect does doubling the radius of a cone's base have on the cone's volume? Thank you! :)
Stacey Warren - Expert brainly.com
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Did you ever think of doubling the radius and calculatng the volume and see what happens to the volume?
Yes, but I don't have a number to work off of.
Let’s take scenario one where we double the height. We know the formula for volume is 1/3 times Pi times R squared times height. All of these are multiplication. So if I double the height, the volume will become 1/3 times Pi times the radius squared times twice the height.
Now, let’s look at scenario two where we double the radius. In this case, the volume is 1/3 times Pi times inch of R. I’ve got two r squared times height which becomes one-third times Pi times four R squared times h which is the same as one third times Pi times r squared times four h. So this is four times the volume of the original one and this is twice the volume of original. Notice 2h, this is 4h. Everything else is the same. So this is one, yeah. 1/3 times Pi times r squared is the same. This is four times height, this is two times height. So, the volume here doubles. Here it’s four times so where the doubling of the height will have the same effect?
No, it would actually quadruple in case we double the radius and double if we double the height.
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So we see that if we double the radius the volume becomes 4 times as great. That is because we replaced r with 2r and then we squared it. So since 2^2 is 4, we introduced a factor of 4 and the volume is 4 times the original volume.
Thanks everyone! :)
When you don't have any numbers to work off of, make up some of your own.