Question

m7 unit 1, lesson 6 comprehension check review
1 look at the circle below. it has a diameter of 20 cm
a = \\(\pi r^{2}\\)
a = \\(\picdot rcdot r\\)
a =
a) what is the approximate area of the circle (numerical)? use 3.14 for \\(\pi\\)
b) what is the exact area of the circle (in terms of \\(\pi\\))?
2 the perez 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 \\(\pi\\)
a) $3226
b) $2010
c) $628
d) $128

Explanation:

Step1: Find radius from diameter for first circle

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

Step2: Calculate approximate area of first circle

Using $\pi = 3.14$ and formula $A=\pi r^{2}$, $A = 3.14\times10^{2}=3.14\times100 = 314$ $cm^{2}$.

Step3: Calculate exact area of first circle

Using formula $A=\pi r^{2}$ with $r = 10$ cm, $A=\pi\times10^{2}=100\pi$ $cm^{2}$.

Step4: Find radius of circular garden

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

Step5: Calculate area of circular garden

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

Step6: Calculate cost of mulch

Cost per square - foot is $\$2.50$. 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) $\$2010$