Question

Sadie is planting a circular garden with diameter of 90 inches. marigolds to fill a sector that has a central angle of 60 degrees. She will plant 5 marigold plants per square foot. How many marigold plants will Sadie need to buy?

Answer 1

Answer: Sadie should buy 37 marigold plants.

Step by step:

First express the area of the full circle (360 degrees, or 2pi radians):

`A_(full)=\pi r^2=\pi((d)/(2))^2=\pi45^2\approx 6361.7\,\,\mbox{in}^2`

A sector with central angle of 60 degrees is a fraction of 60/360=1/6 of the area calculated above, so:

`A_(sector) = (1)/(6) \pi((d)/(2))^2=(1)/(6)\cdot 6361.7\approx 1060.3 \,\,\mbox{in}^2`

The area expressed in sq. ft:

1060.3 sq.in. = 7.36 sq. ft

Given that Sadie plants 5 marigold plants per sq. ft.:

`n = 7.36 \,\,\mbox{ft}^2 \cdot 5 = 36.8\approx 37`

She will need to buy approximately 37 plants