We are given the diameter and height of the tire.
Diameter = 29 in
Height = 8 in
Recall that the surface area of a cylindrical shape is given by
[tex]SA=2\pi r^2+2\pi rh[/tex]
Where r is the radius.
We know that the radius is half of the diameter.
So the surface area becomes
[tex]SA=2\pi(\frac{D}{2})^2+2\pi(\frac{D}{2})h[/tex]
Substitute the values of diameter and height.
[tex]\begin{gathered} SA=2\pi(\frac{29}{2})^2+2\pi(\frac{29}{2})\cdot8 \\ SA=2\pi(14.5)^2+2\pi(14.5)\cdot8 \\ SA=2\pi\cdot210.25^{}+2\pi\cdot116 \\ SA=1321.04^{}+728.85 \\ SA=2049.89\: in^2 \end{gathered}[/tex]
Finally, multiply the surface area by 5 times
[tex]\begin{gathered} SA=2049.89\cdot5 \\ SA=10249.4\: in^2 \end{gathered}[/tex]
Therefore, the tire has covered 10249.4 square inches of space.
