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):

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

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

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

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