Answer:
x=4
y=1
Step-by-step explanation:
In the attached file
The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume
Step-by-step explanation:
Let us revise the rule of surface area and volume of a cylinder
- S.A = 2π r h + 2π r²
- V = π r² h
Forty square inches of material is available to make a cylindrical; can of tuna and water, we need to find the dimensions of the can that will give the most volume
∵ S.A = 40 inches²
∵ S.A = 2π r h + 2π r²
∴ 2π r h + 2π r² = 40
Let us use this rule to find h in terms of r
- Subtract 2π r² from both sides
∵ 2π r h = 40 - 2 π r²
- Divide both sides by 2π r
∴ ![h=\frac{40-2\pi r^{2}}{2\pi r}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B40-2%5Cpi%20r%5E%7B2%7D%7D%7B2%5Cpi%20r%7D)
∴ ![h=\frac{40}{2\pi r}-\frac{2\pi r^{2}}{2\pi r}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B40%7D%7B2%5Cpi%20r%7D-%5Cfrac%7B2%5Cpi%20r%5E%7B2%7D%7D%7B2%5Cpi%20r%7D)
∴ ![h=\frac{20}{\pi r}-r](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B20%7D%7B%5Cpi%20r%7D-r)
∵ V = π r² h
- Substitute h by its value above
∴ ![V=\pi r^{2}(\frac{20}{\pi r}-r)](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7D%28%5Cfrac%7B20%7D%7B%5Cpi%20r%7D-r%29)
∴ V = 20 r - π r³
To find the most volume differentiate it with respect to r and equate it by 0 to find the value of r
∵
= 20 - 3π r²
∵
= 0
∴ 20 - 3π r² = 0
- Add 3π r² to both sides
∴ 20 = 3π r²
- Divide both sides by 3π
∴ r² = 2.122
- Take √ for both sides
∴ r = 1.457 inches
To find h substitute the value of r in the expression of h
∵ ![h=\frac{20}{\pi r}-r](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B20%7D%7B%5Cpi%20r%7D-r)
∴ ![h=\frac{20}{\pi (1.457)}-(1.457)](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B20%7D%7B%5Cpi%20%281.457%29%7D-%281.457%29)
∴ h = 2.913 inches
The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume
Learn more:
You can learn more about volume of solids in brainly.com/question/6443737
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600 lapizes en total okay solo quires que divider 3000 en 5
1200 ÷ 4 = 300
Each person will receive 300 stock cards.
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