Question

A flower garden is shaped like a circle. Its diameter is 38 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd.The gardener is going to cover the path with sand. If one bag of sand can cover 6y * 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 π.)

Answer 1

The answer is 113 bags of sand

Answer 2

The image below will be able to explain the question

Given:

The diameter of the garden is given below as

`\begin{gathered} D=38yd \\ r=(38yd)/(2)=19yd \end{gathered}`

The radius of the big circle will be

`R=19yd+5yd=24yd`

Concept:

To calculate the area of the ring path, we will use the formula below

`Area_{ring\text{ path}}=Area_{big\text{ cirlce}}-A_{small\text{ circle}}`

By substituting the values, we will have

`\begin{gathered} Arean_{ring\text{ path}}=\pi R^2-\pi r^2 \\ \pi=3.14,R=24yd,r=19yd \end{gathered}`

By substituting the values, we will have

`\begin{gathered} Area_{ring\text{ path}}=\pi R^2-\pi r^2 \\ Area_{ring\text{ path}}=3.14*24^2-3.14*19^2 \\ Area_{ring\text{ path}}=1808.64-1133.54 \\ Area_{ring\text{ path}}=675.1yd^2 \end{gathered}`

Given in the question

`6yd^2=1one\text{ bag of sand}`

Let the number of bags of sand for 675.1yd² be

`=x`

By substituting the values, we will have

`\begin{gathered} 6yd^2=1bag\text{ of sand} \\ 675.1yd^2=x\text{ bags of sand} \\ cross\text{ multiply, we will have} \\ 6* x=675.1 \\ 6x=675.1 \\ (6x)/(6)=(675.1)/(6) \\ x=112.5\text{ bags} \\ x=113\text{ bags of sand} \end{gathered}`

Hence,

The final answer is 113 bags of sand