Question

Valerie is putting a swimming pool in the shape of a circle in her back yard. The radius of the pool is 9feet 8 inches. She wants to put in a sidewalk around the pool that is 3 feet wide.Use the feet dimensions and the approximate π ≈3.14 , estimate the total area of the sidewalk. Round to the nearest hundredth.

Answer 1

Answer :Area = 504.06 ft^2

Explanation :

Given :

• The radius of the pool is 9feet 8 inches.

,

• Recall that 1 feet = 12 inches

(Step 1 ) This can be expressed as :

`\begin{gathered} Radius\text{ of the pool = \lparen 9 feet 8 inches \rparen} \\ \text{ = \lparen 9 feet + }(8)/(12)) \\ \text{ = \lparen9 +0.667 \rparen} \\ \text{ = 9.67 feet } \end{gathered}`

(Step 2 ) : Determine outer radius of the sidewalk

`\begin{gathered} Outer\text{ radius = 9.67ft +3 ft} \\ \text{ = 12.67 feet } \end{gathered}`

(Step 3 ) : Estimate the total area of the sidewalk.

• for radius = 12.67 feet

`\begin{gathered} Area\text{ = }\pi *\text{ r }^2 \\ \text{ = 3.14 *\lparen12.67}^2) \\ \text{ =504.06 ft }^2 \\ \text{ }\approx504\text{ .06 }ft\text{ }^2 \\ \end{gathered}`

Area of the total sidewalk = 504.06 ft^2