Answer :
Answer:
Select the cans with a radius of 2.5 in
Explanation:
The volume of a cylinder can be calculated as:
[tex]V=\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the cans. So, solving for h, we get:
[tex]\begin{gathered} \frac{V}{\pi\cdot r^2}=\frac{\pi\cdot r^2\cdot h}{\pi\cdot r^2} \\ \frac{V}{\pi\cdot r^2}=h \end{gathered}[/tex]Therefore, the height for each radius is equal to:
[tex]\begin{gathered} h=\frac{90}{3.14\cdot2^2}=7.16\text{ in} \\ h=\frac{90}{3.14\cdot2.5^2^{}}=4.58\text{ in} \\ h=\frac{90}{3.14\cdot3^2}=\text{ 3.18 in} \\ h=\frac{90}{3.14\cdot3.5^2}=\text{ 2.34 in} \end{gathered}[/tex]Then, the lateral surface for each radius can be calculated as:
[tex]A=2\pi rh[/tex]So, the lateral surface for each cylinder is:
[tex]\begin{gathered} A=2(3.14)(2)(7.16)=90in^2 \\ A=2(3.14)(2.5)(4.58)=72in^2 \\ A=2(3.14)(3)(3.18)=60in^2 \\ A=2(3.14)(3.5)(2.34)=51.43in^2 \end{gathered}[/tex]Therefore, the complete table is:
Radius Height Lateral Sur Volume
2 7.16 in 90 in² 90
2.5 4.58 in 72 in² 90
3 3.28 in 60 in² 90
3.5 51.43 in 51.43 in² 90
So, the company should select the can with a radius of 2.5 in because it has a height lower than 5 in and the lateral surface area is the greatest.