Question

A flower garden is shaped like a circle. Its diameter is 28 yd. A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 36 yd. The gardener is going to cover the path with sand. If one bag of sand can cover 6 yd^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 T.)

Answer 1

67 bags of sand

Step-by-step explanation:

First, we need to calculate the area of the path. So, this area can be calculated as the difference between the area of the circle with a diameter of 36 yd and the area of the circle with 28 yd.

The area of a circle can be calculated as:

`A=\pi\cdot r^2`

Where π is 3.14 and r is the radius of the circle.

The radius of a circle is half the diameter. So, the radius of the circle with a diameter of 36 yd is 18 yd and its area is:

`\begin{gathered} A_1=3.14*(18)^2 \\ A_1=1017.36yd^2 \end{gathered}`

In the same way, the radius of the circle with a diameter of 28 yd is 14 yd and its area is equal to:

`\begin{gathered} A_2=3.14*(14)^2 \\ A_2=615.44yd^2 \end{gathered}`

Then, the area of the path is equal to:

`\begin{gathered} A_1-A_2=1017.36-615.44 \\ A_1-A_2=401.92yd^2 \end{gathered}`

Now, the number of bags of sand can be calculated as:

`\text{Bags = }(401.82yd^2)/(6yd^2)=66.98\approx67\text{ bags of sand}`

Because each bag of sand covers 6 yd².

Therefore, the gardener needs 67 bags of sand