Respuesta :
[tex]\huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}[/tex]
Given :
- volume = 220 in³
- radius = 3 in
Solution :
[tex] \large\boxed{ \mathrm{volume = \pi {r}^{2}h }}[/tex]
- [tex]220 = \dfrac{22}{7} \times 3 \times 3 \times h[/tex]
- [tex] \dfrac{220 \times 7}{22 \times 3 \times 3} = h[/tex]
- [tex] \dfrac{10 \times 7}{3 \times 3} = h[/tex]
- [tex]h = \dfrac{70}{9} [/tex]
- [tex] \boxed{h \: = 7.78 \: \: in}[/tex]
_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
Answer:
0.078 inches
Explanation:
- The volume of a cylinder is [tex]V=\pi r^{2} h[/tex]. [tex]r[/tex] is the radius of the cylinder, [tex]h[/tex] is the height of the cylinder, and [tex]V[/tex] is the total volume.
- We can divide both sides by [tex]9\pi[/tex] to isolate the height. We now have [tex]\frac{220}{9\pi }=h[/tex].
- We can plug in [tex]220[/tex] for the value of [tex]V[/tex], and insert 3 as [tex]r[/tex]. Now, we have [tex]220 = \pi (3^2)(h)[/tex].
- We can simplify the right side by finding the value of [tex]3^2[/tex], which is [tex]3*3[/tex], or [tex]9[/tex]. We now have [tex]220 = 9\pi h[/tex].
- Divide both sides by [tex]9\pi[/tex] so we can isolate the height! We now have [tex]\frac{220}{9\pi }=h[/tex].
- It would be best to use a calculator at this point. Plug the above equation into a calculator; otherwise, replace [tex]\pi[/tex] with [tex]3.14[/tex] and simplify the fraction.
- You should get about [tex]07.7809...[/tex] which we can round to the nearest hundredths (since this is Geometry, I am assuming you know how to round).
- Our final answer is [tex]07.78[/tex] inches.
Hopefully this was of use!
