Question

After heavy rains, a groundskeeper evenly spreads 1,000 pounds of sand over the infield of each baseball diamond in the park. The infield is in the shape of a quarter circle for each baseball diamond.

Which function describes the number of pounds of sand the groundskeeper spreads on each square foot of an infield where the quarter circle has radius
r
feet?


d
(
r
)
=
250
π
r
2


d
(
r
)
=
1
,
000
π
r
2


d
(
r
)
=
250
π
r
2


d
(
r
)
=
4
,
000
π
r
2

Answer 1

Area of a quarter circle = (1/4)πr^2. Sand per square foot = 1000 / [(1/4)πr^2] = 4000/(π r^2).

So d(r) = 4000/(π r^2).