A flower garden is shaped like a circle. Its diameter is 32yd. A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 38yd.
32yd38yd
The gardener is going to cover the path with sand. If one bag of sand can cover 7yd2, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for π.)

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calculista calculista · Answer 1 · 2019-08-31T21:11:55+02:00

Answer:

48 bags

Step-by-step explanation:

step 1

Find the area of the path

we know that

The area of the path is equal to the area of the outer circle minus the area of the inner circle

[tex]A=\pi [rb^{2}-ra^{2}][/tex]

we have

[tex]rb=38/2=19\ yd[/tex] ----> the radius is half the diameter

[tex]ra=32/2=16\ yd[/tex] ----> the radius is half the diameter

[tex]\pi =3.14[/tex]

substitute

[tex]A=3.14 [19^{2}-16^{2}][/tex]

[tex]A=329.7\ yd^2[/tex]

step 2

Find out the number of sand bags needed

we know that

One bag of sand can cover 7 yd^2

so

Divide the total area by 7 to determine the number of bags

[tex]A=329.7/7=47.1\ bags[/tex]

Round up

[tex]48\ bags[/tex]