A farmer has a square lot that is 200 feet on each side. She has a very powerful sprinkler that sprays water in a circle she doesn't want to waste any water, so she'll set her sprinkler so that it doesn't spray any water outside of her lot. What is the largest percentage of her lot that she can water? (Answer to the nearest percent)

Question

Kathleen Cowan

Mathematics

11 April, 22:47

A farmer has a square lot that is 200 feet on each side. She has a very powerful sprinkler that sprays water in a circle she doesn't want to waste any water, so she'll set her sprinkler so that it doesn't spray any water outside of her lot. What is the largest percentage of her lot that she can water? (Answer to the nearest percent)

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Butternut · Answer 1

78.5%

Step-by-step explanation:

Area of a 100ft radius circle = 628sqm

Area of rectangle = 800sqm

= 172sqm difference in size

if 800 sqm = 100%

Then 600 sqm = 3/4 = 75%

60sqm = 3/40 = 7.5%

6sq m = 3/400 = 0.75%

2 sq m = 0.25%

30sqm = 1/2 of 7.5% = 3.75

3.75-0.25 = 3.50%

3.50% + 75 = 78.5%