Hello!
The answer is:
The third option:
2.7 times as much.
Why?
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:
[tex]Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h[/tex]
Where,
[tex]r=radius=\frac{diameter}{2}\\h=height[/tex]
We are given the old can dimensions:
[tex]radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm[/tex]
So, calculating the volume, we have:
[tex]Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}[/tex]
We have that the volume of the old can is:
[tex]Volume_{Can}=199.7cm^{2}[/tex]
New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:
[tex]radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm[/tex]
Calculating we have:
[tex]Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}[/tex]
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:
[tex]\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7[/tex]
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!
