Question

Math Hypothesis What do you think the volume will be if you have a cylindrical pan & a conical pan with the same height and radius? Write your hypothesis using a complete sentence. Prove your hypothesis by showing your math work.

Answer 1

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
`=\pi r^2h`

Volume of cylinder
`=\pi *1^2*3`

Volume of cylinder
`=3\pi`

Volume of cone
`=(1)/(3)\pi r^2h`

Volume of cone
`=(1)/(3)\pi *1^2*3`

Volume of cone
`=\pi`

`3\pi` is clearly more than
`\pi`

Hence volume of cylindrical pan is more than conical pan which proves that my hypothesis is correct.