Answer
l = 24cm
Explanation:
The radius of the cone = 3cm
Surface area = 81 pi squared cm
Surface area of the cone is given as
[tex]\text{Surface area = }\pi rl\text{ + }\pi\cdot r^2[/tex]l = h
r = 3cm
[tex]\begin{gathered} 81\pi\text{ = }\pi(rl+r^2) \\ 81\pi\text{ = }\pi(3\cdot l+3^2) \\ 81\pi\text{ = }\pi(3l\text{ + 9)} \\ \text{Divide both sides by }\pi \\ \frac{81\pi}{\pi}\text{ = }\frac{\pi}{\pi}(3l\text{ + 9)} \\ 81\text{ = 3l + 9} \\ \text{Collect the like terms} \\ 81\text{ - 9 = 3l} \\ 72\text{ = 3l} \\ \text{Divide both sides by 3} \\ l\text{ = }\frac{72}{3} \\ l\text{ = }24\operatorname{cm} \end{gathered}[/tex]Therefore, the slant height is 24cm
