Answer: [tex]\frac{84 ft^{2}}{r}-r[/tex]
Step-by-step explanation:
The surface area of a cone is given by the following formula:
[tex]A_{cone}=\pi r^{2}+\pi L r[/tex] (1)
Where:
[tex]A_{cone}=84 \pi ft^{2}[/tex] is the surface area
[tex]r[/tex] is the radius of the base of the cone (assuming it is a circumference)
[tex]L[/tex] is the slant height
Rewriting (1):
[tex]84 \pi ft^{2}=\pi r^{2}+\pi L r[/tex] (2)
Isolating [tex]L[/tex]:
[tex]L=\frac{84 ft^{2}}{r}-r[/tex] This is the slant height of the cone in termsof [tex]r[/tex]
