Question

15. During the spring semester, the Sustainability Club plants a flower bed in BHCC's gardenarea outside of the Health and Wellness Center using the dimensions shown in the diagramArea of a circle: A = tr' (use 3.14 to approximate the value of T)a) What is the area of the flowerbed?b) If they use fertilizer at the rate of 1 cup for 15 square feet, how many cups will theyneed for the flowerbed?

Answer 1

Given the area of the circle as shown below

`A=\pi r^2`

a) To find the area of the flower bed, we will find the area of the circle and divide the result by 4, since one flower bed is a quarter of the circle.

`\begin{gathered} A=\pi r^2 \\ \pi=3.14 \\ r=5ft \end{gathered}`
`\begin{gathered} A=3.14*5^2 \\ A=3.14*25 \\ A=78.5ft^2 \end{gathered}`

Hence,the area of a flower bed is

`\begin{gathered} A_(f\Rightarrow)(A)/(4)=(78.5ft^2)/(4) \\ \\ A_f=19.625ft^2 \end{gathered}`

b) Given that the rate of fertilizer used is 1 cup per 15 square feet, thus, it will take x cups for 19.625 square feet. To find x, we will have:

`\begin{gathered} 1\rightarrow15ft^2 \\ x\rightarrow19.625ft^2 \\ \text{cross multiply} \\ 15xft^2=19.625ft^2 \\ x=(19.625)/(15) \\ x=1.308\text{cups} \end{gathered}`

Hence, they will need 1.308 cups for the flower bed.