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aksik [14]
4 years ago
10

Can someone help and check my work. thank you

Mathematics
1 answer:
docker41 [41]4 years ago
7 0
Everything looks good but the only thing you didn't do in the very last step is to cancel out the 5 in both the numerator and denominator.  Everything is being multiplied together so you're not doing anything "illegal" by canceling the 5's.  In fact, if you're simplifying, you NEED to cancel the 5's.
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Check the picture below.

\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill

\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}

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