Question

1. look at the circle below. it has a diameter of 20 cm. a) what is the approximate area of the circle (numerical)? use 3.14 for π. b) what is the exact area of the circle (in terms of π)? 2. the peroz family has a circular garden with a diameter of 32 ft. they want to cover the whole garden with mulch. the cost of mulch is $2.50 per square - foot. rounding to the nearest dollar, how much will it cost to cover the entire garden with mulch? use 3.14 for π. a) $3225 b) $2010 c) $628 d) $128

Explanation:

Step1: Find the radius of the first - circle

Given diameter $d = 20$ cm, radius $r=\frac{d}{2}=\frac{20}{2}=10$ cm.

Step2: Calculate the approximate area of the first - circle

The formula for the area of a circle is $A=\pi r^{2}$. Using $\pi = 3.14$ and $r = 10$ cm, we have $A=3.14\times10^{2}=3.14\times100 = 314$ $cm^{2}$.

Step3: Calculate the exact area of the first - circle

Using the formula $A=\pi r^{2}$ with $r = 10$ cm, the exact area $A = 100\pi$ $cm^{2}$.

Step4: Find the radius of the second - circle

Given diameter $d = 32$ ft, radius $r=\frac{d}{2}=\frac{32}{2}=16$ ft.

Step5: Calculate the area of the second - circle

Using the formula $A=\pi r^{2}$ and $\pi = 3.14$, we get $A=3.14\times16^{2}=3.14\times256 = 803.84$ $ft^{2}$.

Step6: Calculate the cost of mulch

The cost of mulch is $\$2.50$ per square - foot. So the total cost $C=2.50\times A=2.50\times803.84 = 2009.6\approx2010$ dollars.

Answer:

1. A) $314$ $cm^{2}$

B) $100\pi$ $cm^{2}$

1. B. $\$2010$