Question

1. calculate the radius of the following circles, using the area given each time. (/3 marks)

a) area = 17.35m²
b) area = 214.86m²
c) area = 490.87cm²

Explanation:

Step1: Recall circle area formula

The area of a circle is $A = \pi r^2$, rearranged to solve for radius: $r = \sqrt{\frac{A}{\pi}}$
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Part a)

Step1: Substitute $A=17.35\text{m}^2$

$r = \sqrt{\frac{17.35}{\pi}}$

Step2: Compute the value

$r = \sqrt{\frac{17.35}{3.1416}} \approx \sqrt{5.5226} \approx 2.35\text{m}$

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Part b)

Step1: Substitute $A=214.86\text{m}^2$

$r = \sqrt{\frac{214.86}{\pi}}$

Step2: Compute the value

$r = \sqrt{\frac{214.86}{3.1416}} \approx \sqrt{68.39} \approx 8.27\text{m}$

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Part c)

Step1: Substitute $A=490.87\text{cm}^2$

$r = \sqrt{\frac{490.87}{\pi}}$

Step2: Compute the value

$r = \sqrt{\frac{490.87}{3.1416}} \approx \sqrt{156.25} \approx 12.5\text{cm}$

Answer:

a) $\approx 2.35\text{m}$
b) $\approx 8.27\text{m}$
c) $\approx 12.5\text{cm}$