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At the park there is a pool shaped like a circle with radius 10 yd. A ring-shaped path goes around the pool. Its width is 5 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 7y * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.

At the park there is a pool shaped like a circle with radius 10 yd A ringshaped path goes around the pool Its width is 5 ydWe are going to give a new layer of c class=


Answer :

Solution

Step 1:

Concept

[tex]Area\text{ of the colored path = Area of inner circle - Area of outer circle}[/tex]

Step 2:

[tex]\begin{gathered} Inner\text{ radius r = 10 yd} \\ Outer\text{ radius R = 15 yd} \\ \pi\text{ = 3.14} \end{gathered}[/tex]

Step 3:

Substitute in the formula to find the area of the colored part.

[tex]\begin{gathered} Area\text{ of the colored part = 3.14}\times15^2\text{ - 3.14}\times10^2 \\ =\text{ 706.5 - 314} \\ =\text{ 392.5 yd}^2 \end{gathered}[/tex][tex]\begin{gathered} Number\text{ of gallons of coating needed =}\frac{392.5}{7} \\ =\text{ 56.071428571 gallons} \end{gathered}[/tex]

Final answer

57 gallons

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