SOLUTION: A 39-ounce can of Hills Bros.® coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius?
[Hint: The surface area S of a right cylinder is
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[Hint: The surface area S of a right cylinder is
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Question 1207769: A 39-ounce can of Hills Bros.® coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius?
[Hint: The surface area S of a right cylinder is S = 2(pi)(r^2) + 2(pi)rh, where r is the radius and h is the height.
I say the set up I'd this:
188.5 = 2(pi)(r^2) + 2(pi)7r
I now must find r.
Yes? Found 3 solutions by mananth, math_tutor2020, ikleyn:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
S = 2pi*r^2 + 2pi*r*h
S = 2pi*r(r + h)
188.5 = 2pi*r(r + 7)
r(r+7) = 188.5/(2pi)
r(r+7) = 30.00070677 approximately
I used my calculator's stored version of pi to get the most accuracy possible when computing the right hand side.
If we rounded to say 1 decimal place, then that 30.00070677 becomes 30.0 or simply 30.
I'm rounding to one decimal place because 188.5 is to the same level of accuracy.
Please let me know if your teacher wants some other level of accuracy instead.
r(r+7) = 30
r^2+7r = 30
r^2+7r-30 = 0
(r+10)(r-3) = 0
r+10 = 0 or r-3 = 0
r = -10 or r = 3
A negative radius is not possible. We'll ignore it.
The only practical solution is r = 3.
Let's check this radius.
S = 2pi*r^2 + 2pi*r*h
S = 2pi*r(r + h)
S = 2pi*3(3+7)
S = 60pi
S = 188.49555922 approximately when using a calculator
S = 188.5 when rounding to one decimal place.
This confirms we have the correct radius value when considering the rounding method mentioned.
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