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jok3333 [9.3K]
3 years ago
13

Help please and thanks! I'll award brainliest if you show your work as well :)

Mathematics
1 answer:
iren2701 [21]3 years ago
8 0

Answer:

6 inches

Step-by-step explanation:

Formula for surface area of a cylinder:

SA=2\pi r^{2} +2\pi rh

Plug in values and solve for the radius:

180\pi =2\pi r^{2} +2\pi r(9)\\

Divide both sides by 2\pi

90=r^{2} +r(9)

Subtract 90 from both sides

0=r^{2} +9r-90

Use the quadratic equation to find the roots

x=(-b±\sqrt{b^2-4ac})*\frac{1}{2a} (sorry for formatting, Brainly doesn't

                                           allow equations with ± in them)

x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}        and          x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}

x=\frac{(-9+\sqrt{81+360})}{2}          and          x=\frac{(-9-\sqrt{81+360})}{2}

x=\frac{(-9+\sqrt{441})}{2}               and          x=\frac{(-9-\sqrt{441})}{2}

x=\frac{(-9+21)}{2}                   and          x=\frac{(-9-21)}{2}

x=\frac{12}{2}                           and          x=\frac{-30}{2}

x=6                             and          x=-15  

We can't have a negative radius, so that leaves us with r=6 in.

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Since we know that perfect square trinomial formula states that any trinomial of the form ax^{2} +bx+c is said to a perfect square if it satisfies the condition b^{2} =4ac.

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