Question

Melvin is pushing a tire during a workout with the dimension shown.How many square inches of space has the tire covered after Melvin pushes the tire 5 times around. Round to the nearest tenths

Answer 1

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

`SA=2\pi r^2+2\pi rh`

Where r is the radius.

We know that the radius is half of the diameter.

So the surface area becomes

`SA=2\pi((D)/(2))^2+2\pi((D)/(2))h`

Substitute the values of diameter and height.

`\begin{gathered} SA=2\pi((29)/(2))^2+2\pi((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}`

Finally, multiply the surface area by 5 times

`\begin{gathered} SA=2049.89\cdot5 \\ SA=10249.4\: in^2 \end{gathered}`

Therefore, the tire has covered 10249.4 square inches of space.