a right cone has the volume of 333 cubic yards. if a right cylinder had the same height and base, what would be the volume of the cylinder?

Question

algebra question

Answer 1

This is actually a bit deceiving, the math is easier than you would think!

 

The volume for a cone is 333 yd³ and the equation is πr²•(h/3) so V_rc= πr² (h/3). So far so good? The Volume for the cylinder is πr² h, with the base and the height being the same as the cone's.

 

You might think that you would have to use the same volume (333 yd³) and work out the math to find h and base and make sure it works for both equations, but you don't (and can't)!

Here's why: neither the radius nor the height was given, so you can't solve for h or r through substitution.

 

The math is easier than you might think because of how similar the equations are. πr² (h/3) is almost exactly like πr² h. The only difference is that the h of the cone is divided by 3 while the height for the cylinder is on its own. This means that it would take 3 times the value for the height to equal that for the cylinder. Since you know V_rc=333yd³ then V_cyl=999 yd³ (333•3=999)!

 

Here's the algebra so you can see why it works out that way:

 

V_rc= πr² (h/3)=333 yd³             V_cyl= πr²h

 

to get rid of the the fraction, multiply both sides by 3 for Vrc

 

πr² (h/3) •3=333 yd³ •3 which is 999 yd³

 

base (πr²) and height (h) are the same for both, so now...

 

πr²•h [of cone]= πr²h [of cylinder] which is a true statement! So that's it!