6) A square rock garden with sides of 110 feet is placed in the middle of a circ

Question

6) A square rock garden with sides of 110 feet is placed in the middle of a circular grass yard. If the circumference of the yard is 550 feet, then how much area is covered by grass? For all calculations involving T, use T 3.14. Hint: Be careful that you do not do any rounding on answers until the very end of a problem part, or you could create rounding error a) Amount of area covered by grass, measured in square feet F square feet. DO NOT TYPE COMMAS. Round your answer to 2 decimal places as needed. b) Amount of area covered by grass, measured in square yards square yards. Round your answer to 2 decimal places as needed

Explanation / Answer

Circumference of yard = 550 feet

Circumference of circle = 2pi * r
550 = 2 * 3.14 * r
r = 87.579

Area of circle = pi * r^2
= 3.14 * (87.579)^2
= 24084.39

square rock garden sides = 110 feet
Area of square = side^2
= (110)^2
= 12100

a) Amount of area covered by grass = area of circle - area of square
= 24084.39 - 12100
= 11984.39 square feet

b)
Amount of area covered by grass = area of circle - area of square
= (24084.39 - 12100)*0.3333
= 3994.79square yrds

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