In order to calculate the volume of a cylinder, we can use the following formula:
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
Where r is the base radius and h is the height.
If the circumference is 8, we have:
![\begin{gathered} C=2\pi r \\ 8=2\pi r \\ r=\frac{4}{\pi} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20C%3D2%5Cpi%20r%20%5C%5C%208%3D2%5Cpi%20r%20%5C%5C%20r%3D%5Cfrac%7B4%7D%7B%5Cpi%7D%20%5Cend%7Bgathered%7D)
Now, calculating the volume, we have:
![\begin{gathered} V=\pi(\frac{4}{\pi})^2\cdot10 \\ V=\frac{160}{\pi} \\ V=50.93 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D%5Cpi%28%5Cfrac%7B4%7D%7B%5Cpi%7D%29%5E2%5Ccdot10%20%5C%5C%20V%3D%5Cfrac%7B160%7D%7B%5Cpi%7D%20%5C%5C%20V%3D50.93%20%5Cend%7Bgathered%7D)
So the correct option is the second one.
Answer:
![72\pi\ in^{3}](https://tex.z-dn.net/?f=72%5Cpi%5C%20in%5E%7B3%7D)
Step-by-step explanation:
step 1
<em>Calculate the volume of the cylinder (flower vase)</em>
The volume is equal to
![V=\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7Dh)
we have
-----> the radius is half the diameter
![h=12\ in](https://tex.z-dn.net/?f=h%3D12%5C%20in)
substitute the values
------> exact value
step 2
Calculate 2/3 of the volume
![V=(2/3)108\pi=72\pi\ in^{3}](https://tex.z-dn.net/?f=V%3D%282%2F3%29108%5Cpi%3D72%5Cpi%5C%20in%5E%7B3%7D)
The nearest whole number would be 93 because you round up if the decimal place is greater than 5 and down if it's less.
So I would say 4/18 but it could probably be 18/81 to
Step-by-step explanation:
we divide both sides by 4 to single out the X
(4X) / 4 = (2/3)/4
simplify
X = 2/12