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valkas [14]
3 years ago
14

For a right circular cone, if the radius is reduced to 1/5 its original size and the slant height is reduced to 1/6 its original

size, find the surface area if the original radius is 8 centimeters and the original slant height is 13 centimeters.

Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0
Check the picture below.

\bf \begin{cases}
\underline{r=8}\\
\frac{1}{5}r\implies \frac{1}{5}\cdot 8\\
r=\frac{8}{5}\\
--------\\
z=slant\ height\\
\underline{z=13}\\
\frac{1}{6}z\implies \frac{1}{6}\cdot 13\\
z=\frac{13}{6}
\end{cases}\qquad 
\begin{array}{llll}
S=\pi rz+\pi r^2
\\\\\\
S=\pi \cdot \cfrac{8}{5}\cdot \cfrac{13}{6}+\pi \cdot \left( \cfrac{8}{5} \right)^2
\end{array}
\\\\\\
S=\cfrac{104\pi }{30}+\cfrac{8^2}{5^2}\implies S=\cfrac{104\pi }{30}+\cfrac{64}{25}\implies S=\cfrac{520\pi +384}{150}

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