Question

Trees are to be planted inside a circular tree orchard so that there are $5$ trees per square meter. The circumference of the tree orchard is $30$ meters. If trees are available only in allotments of packages of $6$, how many allotments will the caretaker need to purchase?

• A. $59$
• B. $117$
• C. $58$
• D. $60$
• E. $118$

Answer 1

Answer: (D)

$60$

Circumference is $30=2\pi r$ , which gives $r=\frac{15}{\pi }$
Area of tree orchard will be $\pi r^2=\frac{225}{\pi }$
Given that there are $5$ trees per square meter, so for $\frac{225}{\pi }$ square meters, we have $\frac{225}{\pi }\times 5=358.1$
Given that trees are available in pack of $6$
So number of packs needed is $\frac{358.1}{6}=59.35$, which implies we need $60$ allotments