The time it will take Jesse to finish sanding the table is approximately 22.61 hours.
Suppose the circle has radius of 'r' units, then, its area is given as:
[tex]A = \pi \times (r)^2[/tex] sq. units
Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:
[tex]A = \pi \times (\dfrac{d}{2})^2[/tex] sq. units
For the given case, sanding being done needs to be equal to the area of the circular table, as it has to be done for whole table's surface, which is circular, and area of sanding done will be equal to the area of that circular table.
The area of table(diameter given as 6 ft) is: [tex]A = \pi \times (\dfrac{d}{2})^2 \approx 3.14 \times 6^2 = 113.04 \: \rm ft^2[/tex]
Since Jesse does 5 sq. feet per hour, let she takes T hours time to finish sanding the table, then we have:
[tex]\rm T \times 5\: ft^2 = A \approx 113.04 \: ft^2\\\\\text{Dividing all sides by 5, we get}\\\\T = \dfrac{113.04}{5} \approx 22.61 \: hours[/tex]
(since 5 sq. feet in 1 hours, then in T hours, T times 5 sq. feet will be done which is equal to area of table, as in approx T hours, she finishes sanding the table)
Thus, it will take approx 22.61 hours for Jesse to finish sanding the table.
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