part 3 of 3\na manufacturer can save money by making a can that maximizes volume and minimizes the amount of…

part 3 of 3\na manufacturer can save money by making a can that maximizes volume and minimizes the amount of metal used. for a can with radius r and height h, this goal is reached when 2πr² = πr²h. answer parts a and b below\n(simplify your answer.)\nb. the height is 2 times the radius.\n(simplify your answer.)\nc. the height is units greater than the radius.\n(simplify your answer.)\nd. the height is equal to the radius.\nb. the area of a label for a can is a = 2πrh. use your result from part a to write a formula giving the area a of a label for a can that meets the manufacturers goals. express your answer using a single variable.\na = (simplify your answer. type an exact answer, using π as needed.)

part 3 of 3\na manufacturer can save money by making a can that maximizes volume and minimizes the amount of metal used. for a can with radius r and height h, this goal is reached when 2πr² = πr²h. answer parts a and b below\n(simplify your answer.)\nb. the height is 2 times the radius.\n(simplify your answer.)\nc. the height is units greater than the radius.\n(simplify your answer.)\nd. the height is equal to the radius.\nb. the area of a label for a can is a = 2πrh. use your result from part a to write a formula giving the area a of a label for a can that meets the manufacturers goals. express your answer using a single variable.\na = (simplify your answer. type an exact answer, using π as needed.)

Answer

Explanation:

Step1: Solve for h in the given equation

Given $2\pi r^{2}=\pi r^{2}h$. Divide both sides by $\pi r^{2}$ (assuming $r\neq0$). We get $h = 2$. So the height is 2 times the radius.

Step2: Substitute h into the label - area formula

The area of the label is $A = 2\pi rh$. Since $h = 2r$ from part a, substitute $h$: $A=2\pi r\times(2r)=4\pi r^{2}$.

Answer:

a. B. The height is 2 times the radius. b. $A = 4\pi r^{2}$