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A cylindrical cup measures 12cm in height.  When filled to the very top, it holds 780 cubic centimeters of water.  What is the radius of the cup, rounded to the nearest tenth?

 May 30, 2023
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Hello! Let me know if you find any errors in my solution.

 

The volume of a cylinder = \(\pi r^2h\)

 

We know:

\(v = 780 cm^3\)

\(h = 12cm\)

 

Now we plug in those values:
\(780 cm^3 = \pi r^2 12\)

 

And isolate the variable r:

 

\(\frac{780 cm^3}{12cm} = \pi r^2 \\\frac{65cm^2}{\pi} = r^2 \\r = \frac{\sqrt{65}cm}{\pi}\)

 

And round the radius to the nearest tenth:

 

\(r = \frac{\sqrt{65}}{\pi} \\r \approx \frac{8.1}{\pi} \\\pi \approx 3.1 \\r \approx \frac{8.1}{3.1} \approx \boxed{2.6 cm}\)

 

Therefore, the answer is \(\boxed{2.6 cm}\)

 May 30, 2023
edited by supremecheetah  May 30, 2023
edited by supremecheetah  May 30, 2023

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