Question

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.

Answer 1

check the picture below.


`\bf \begin{cases} \underline{r=8}\\ (1)/(5)r\implies (1)/(5)\cdot 8\\ r=(8)/(5)\\ --------\\ z=slant\ height\\ \underline{z=13}\\ (1)/(6)z\implies (1)/(6)\cdot 13\\ z=(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}`