Question

A flower garden is shaped like a circle. Its diameter is 24 yd. A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 30 yd.The gardener is going to cover the path with sand. If one bag of sand can cover 8y * d ^ 2 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 it.)

Answer 1

- The bags of sand are going to be used to cover the expanse or area in form of a ring. This means that the area of the ring path must be the same area covered.

- This means that we must find the area of the ring. The area of the ring is simply gotten by subtracting the area of the smaller circle from that of the bigger circle.

- After getting this area, we can then assess how many 8yd² bags of sand can fill up this area.

- Thus, with the steps outlined above, we can proceed to solve the question.

- The area of a circle is given by:

`\begin{gathered} A=\pi* r^2 \\ where, \\ r=radius\text{ of the circle} \end{gathered}`

- Thus, we can find the areas of the small and large circles as follows:

`\begin{gathered} r_(small)=(24)/(2)=12 \\ \therefore A_(small)=\pi* r_(small)^2 \\ \\ A_(small)=\pi*12^2=144\pi \\ \\ \\ r_(large)=(30)/(2)=15 \\ \therefore A_(large)=\pi* r^2_(large) \\ \\ A_(large)=\pi*15^2=225\pi \end{gathered}`

- Now that we have the areas of both circles, we can proceed to find the area of the ring path by subtracting as follows:

`\begin{gathered} A_(ring)=A_(large)-A_(small) \\ A_(ring)=225\pi-144\pi \\ \\ \therefore A_(ring)=81\pi \end{gathered}`

- This is the area of the ring path

- In order for us to know how many bags containing 8yds² of sand will fill up the ring path, we can simply divide the area of the ring path by the area of the bag of sand.

- That is,

`\text{ Number of bags needed }=\frac{Area\text{ of ring Path}}{Area\text{ of one bag of sand}}`

- The number of bags needed can thus be calculated as follows:

- Thus, the number of bags needed is 32

Final Answer

The number of bags needed by the gardener is 32