<h2>
Hello!</h2>
The answer is:
The third option:
2.7 times as much.
<h2>
Why?</h2>
To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.
So, calculating we have:
Old can:
Since the cans have a right cylinder shape, we can calculate their volume using the following formula:
![Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h](https://tex.z-dn.net/?f=Volume_%7BRightCylinder%7D%3DVolume_%7BCan%7D%3D%5Cpi%20r%5E%7B2%7D%20h)
Where,
![r=radius=\frac{diameter}{2}\\h=height](https://tex.z-dn.net/?f=r%3Dradius%3D%5Cfrac%7Bdiameter%7D%7B2%7D%5C%5Ch%3Dheight)
We are given the old can dimensions:
![radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm](https://tex.z-dn.net/?f=radius%3D%5Cfrac%7B5.2cm%7D%7B2%7D%3D2.6cm%5C%5C%5C%5Cheight%3D9.4cm)
So, calculating the volume, we have:
![Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}](https://tex.z-dn.net/?f=Volume_%7BCan%7D%3D%5Cpi%20%2A2.6cm%5E%7B2%7D%20%2A9.4cm%3D199.7cm%5E%7B3%7D)
We have that the volume of the old can is:
![Volume_{Can}=199.7cm^{2}](https://tex.z-dn.net/?f=Volume_%7BCan%7D%3D199.7cm%5E%7B2%7D)
New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:
![radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm](https://tex.z-dn.net/?f=radius%3D%5Cfrac%7B8.5cm%7D%7B2%7D%3D4.25cm%5C%5C%5C%5Cheight%3D9.4cm)
Calculating we have:
![Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}](https://tex.z-dn.net/?f=Volume_%7BCan%7D%3D%5Cpi%20%2A4.25cm%5E%7B2%7D%20%2A9.4cm%3D533.40cm%5E%7B3%7D)
Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:
![\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7](https://tex.z-dn.net/?f=%5Cfrac%7B533.4cm%5E%7B3%7D%20%7D%7B199.7cm%5E%7B3%7D%7D%3D2.67%3D2.7)
Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:
2.7 times as much.
Have a nice day!