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# I know I don't ask questions, but...

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Find the diameter of a right cone with a slant height of $$18cm$$ and a surface area of $$208\pi cm^2$$.

May 22, 2017

#1
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Find the diameter of a right cone with a slant height 18cm of  and a surface area of 208 pi cm2.

May 22, 2017
#3
+2440
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Thank you. I knew that the surface area equals the circumference of the base multiplied by the slant height and then add the area of the base. I didn't realize that I could setup an equation with that information, though...

TheXSquaredFactor  May 22, 2017
#1
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Find the diameter of a right cone with a slant height of  $$18\ cm$$ and a surface area of $$208 \pi \ cm^2$$.

Surface area of cone $$A = \pi r^2+\pi rl$$

$$\begin{array}{|rcll|} \hline \pi r^2+ \pi rl &=& A \quad & | \quad : \pi \\ r^2+rl &=& \frac{A}{\pi} \\ r^2+rl -\frac{A}{\pi} &=& 0 \\ r &=& \frac{-l\pm \sqrt{l^2-4\cdot (-\frac{A}{\pi}) } } {2} \\ r &=& \frac{-l\pm \sqrt{l^2+ \frac{4A}{\pi} } } {2} \\ 2r = d &=& -l\pm \sqrt{l^2+ \frac{4A}{\pi} } \quad & | \quad A = 280\pi \qquad l = 18 \\ d &=& -18\pm \sqrt{18^2+ 4\cdot 208 } \\ d &=& -18\pm \sqrt{1156 } \\ d &=& -18\pm 34 \\ d &=& -18 + 34 \\ d &=& 16 \\ \hline \end{array}$$

The diameter  is 16 cm

heureka May 22, 2017
#3
+2440
0

Thank you. I knew that the surface area equals the circumference of the base multiplied by the slant height and then add the area of the base. I didn't realize that I could setup an equation with that information, though...

TheXSquaredFactor  May 22, 2017