Question

At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its width is 6 yd.
We are going to give a new layer of coating to the path. If one gallon of coating can cover 5 yd", how many gallons of coating do we need? Note that coating
comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for n).

Answer 1

Answer:

106 gal

Step-by-step explanation:

step 1

Find the area of the path

we know that

The area of the path is given by the formula

$A=\pi r_2^{2} -\pi r_1^{2}$

$A=\pi [r_2^{2} -r_1^{2}]$

where

r_2 is the radius of the pool plus the width of the path

r_1 is the radius of the pool

we have

$r_1=22/2=11\ yd$ ---> the radius is half the diameter

$r_2=11+6=17\ yd$

substitute

$A=\pi [17^{2}-11^{2}]$

$A=168\pi\ yd^2$

assume

$\pi =3.14$

$A=168(3.14)=527.52\ yd^2$

step 2

Find the gallons of coating needed

Divide the area of the path by 5

so

$527.52/5=105.5\ gal$

Round up

therefore

106 gal