Question 1207769
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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.



Answer: 3 inches
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