Find the radius of a right cylinder with a height of 5 feet and surface area 208pi
This problem
is based on the"Surface Area of a Right Cylinder" Therom
My study guide tells me the radius is 8 Feet,
However how did they solve this,
I have written out equation 208pi = 2pir^2 + 2pir(5) How do I solve for r (radius)?
If someone could provide a written-out solution I would really appreciate it, thank you kindly.
What is the radius of this right cylinder?
2021-04-05 8:41 am
回答 (3)
2021-04-05 8:46 am
✔ 最佳答案
it's not a theorem, it's a fact.A = 2πr² + 2πrh = 2πr(r+h)
2πr(r+5) = 208π
r(r+5) = 104
r² + 5r – 104 = 0
(r – 8)(r + 13)
r = 8, – 13
skipping the negative answer, r = 8 ft
2021-04-05 1:41 pm
The surface area of a right cylinder is the sum of the areas of the two circular ends (πr^2 and πr^2) and the area of the rectangular edge (circumference x height).
208π = πr^2 + πr^2 + (2πr)(5)
Start by dividing through by 2π and subtracting the constant.
208π = 2πr^2 + 2πr(5)
104 = r^2 + 5r
0 = r^2 + 5r - 104
Next either apply the quadratic formula, or factor the polynomial.
r = (-5 ± √[5^2 - 4(1)(-104)] ) / 2(1)
r = 8 or -13
Negative solutions are invalid for questions like the radius of an object, so the only solution is r=8.
208π = πr^2 + πr^2 + (2πr)(5)
Start by dividing through by 2π and subtracting the constant.
208π = 2πr^2 + 2πr(5)
104 = r^2 + 5r
0 = r^2 + 5r - 104
Next either apply the quadratic formula, or factor the polynomial.
r = (-5 ± √[5^2 - 4(1)(-104)] ) / 2(1)
r = 8 or -13
Negative solutions are invalid for questions like the radius of an object, so the only solution is r=8.
2021-04-05 10:12 am
The radius of a right cylinder
with a height of 5 feet and surface area 208π
208π = 2π r^2 + 2π r (5)
r = 8 feet
with a height of 5 feet and surface area 208π
208π = 2π r^2 + 2π r (5)
r = 8 feet
收錄日期: 2021-04-24 08:39:12
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