Answer:
Approximately the volume of cone-shaped container is <u>393 in³</u>.
Step-by-step explanation:
Given:
A company makes a cone-shaped container with a height of 15 in.
The area of its base is about 78.8 in².
Now, to get the cone-shaped container volume.
So, we find the radius first by using formula:
Let the radius be ![r.](https://tex.z-dn.net/?f=r.)
<u><em>(Using the value π = 3.14)</em></u>
![A_{B}=78.8\ in^2.](https://tex.z-dn.net/?f=A_%7BB%7D%3D78.8%5C%20in%5E2.)
![A_{B}=\pi r^2](https://tex.z-dn.net/?f=A_%7BB%7D%3D%5Cpi%20r%5E2)
![78.8=3.14\times r^2](https://tex.z-dn.net/?f=78.8%3D3.14%5Ctimes%20r%5E2)
<em>Dividing both sides by 3.14 we get:</em>
<em />
<em />
<em>Using square root on both sides we get:</em>
![5.00=r](https://tex.z-dn.net/?f=5.00%3Dr)
![r=5\ in.](https://tex.z-dn.net/?f=r%3D5%5C%20in.)
Thus, the radius (
) = 5 in.
<u>The height (</u>
<u>) = 15 in.</u>
Now, to get the volume of the cone-shaped container 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 5^2\times \frac{15}{3} \\\\Volume=3.14\times 25\times 5\\\\Volume=392.50\ in^3.](https://tex.z-dn.net/?f=Volume%3D3.14%5Ctimes%205%5E2%5Ctimes%20%5Cfrac%7B15%7D%7B3%7D%20%5C%5C%5C%5CVolume%3D3.14%5Ctimes%2025%5Ctimes%205%5C%5C%5C%5CVolume%3D392.50%5C%20in%5E3.)
Therefore, approximately the volume of the cone-shaped container is 393 in³.