Answer:
The plastic cylindrical cup will hold <u>17.96 ounces</u> of water.
Step-by-step explanation:
Given:
A 6 oz paper cup is shaped like a cone with a diameter of 4 inches.
Now, to find ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup.
Volume of cone = 6 oz.
Diameter = 4 inches.
So, radius (r) = ![\frac{Diameter}{2} =\frac{4}{2} =2\ inches.](https://tex.z-dn.net/?f=%5Cfrac%7BDiameter%7D%7B2%7D%20%3D%5Cfrac%7B4%7D%7B2%7D%20%3D2%5C%20inches.)
<u><em>Taking the value </em></u>
<u><em> = 3.14.</em></u>
Now, to get the height (h) we put formula:
![Volume=\pi r^2\frac{h}{3}](https://tex.z-dn.net/?f=Volume%3D%5Cpi%20r%5E2%5Cfrac%7Bh%7D%7B3%7D)
![Volume=3.14\times 2^2\times \frac{h}{3}](https://tex.z-dn.net/?f=Volume%3D3.14%5Ctimes%202%5E2%5Ctimes%20%5Cfrac%7Bh%7D%7B3%7D)
![6=3.14\times 4\times \frac{h}{3}](https://tex.z-dn.net/?f=6%3D3.14%5Ctimes%204%5Ctimes%20%5Cfrac%7Bh%7D%7B3%7D)
<em>Multiplying both sides by 3 we get:</em>
![18=12.56h](https://tex.z-dn.net/?f=18%3D12.56h)
<em>Dividing both sides by 12.56 we get:</em>
![1.43=h](https://tex.z-dn.net/?f=1.43%3Dh)
![h=1.43\ inches.](https://tex.z-dn.net/?f=h%3D1.43%5C%20inches.)
Now, to get the volume of cylindrical cup.
As, given it is the same height as the paper cup.
Height (h) = 1.43 inches.
Diameter = 4 inches.
Radius (r) = ![\frac{Diameter}{2} =\frac{4}{2} =2\ inches.](https://tex.z-dn.net/?f=%5Cfrac%7BDiameter%7D%7B2%7D%20%3D%5Cfrac%7B4%7D%7B2%7D%20%3D2%5C%20inches.)
So, we put formula to get the ounces of water a plastic cylindrical cup will hold:
![Volume =\pi r^2h](https://tex.z-dn.net/?f=Volume%20%3D%5Cpi%20r%5E2h)
![Volume=3.14\times 2^2\times 1.43](https://tex.z-dn.net/?f=Volume%3D3.14%5Ctimes%202%5E2%5Ctimes%201.43)
![Volume=3.14\times 4\times 1.43](https://tex.z-dn.net/?f=Volume%3D3.14%5Ctimes%204%5Ctimes%201.43)
![Volume=17.96\ oz.](https://tex.z-dn.net/?f=Volume%3D17.96%5C%20oz.)
Therefore, the plastic cylindrical cup will hold 17.96 ounces of water.