Question says that you have a cylindrical pan and a conical pan with the same height and radius.
Now we have to compare the volume of both type of pan and justify that using mathematical calculations.
Hypothesis:
I would say that cylindrical pan will have more volume than conical pan volume because of larger size.
Proof:
Given that diameter of both = 2 in
then radius r=diameter/2=2/2= 1 in
we can use formula of volume of each to find the volume of each can as shown below:
Volume of cylinder [tex]=\pi r^2h[/tex]
Volume of cylinder [tex]=\pi *1^2*3[/tex]
Volume of cylinder [tex]=3\pi[/tex]
Volume of cone [tex]=\frac{1}{3}\pi r^2h[/tex]
Volume of cone [tex]=\frac{1}{3}\pi *1^2*3[/tex]
Volume of cone [tex]=\pi[/tex]
[tex]3\pi[/tex] is clearly more than [tex]\pi[/tex]
Hence volume of cylindrical pan is more than conical pan which proves that my hypothesis is correct.
