Question #ef5d9

#"area of sector "=" area of circle "xx140/360#

#"the required area is in square feet"#

#rArrd=60" inches "=5" feet "#

#rArr" radius "r=5/2=2.5" feet"#

#rArr"area of sector "=(pixx(2.5)^2xx140)/360#

#color(white)(xxxxxxxxxxxxx)~~7.64" square feet"#

#"1 square foot "to" 7 plants"#

#rArr7.64" square feet "to7/1xx7.64=53.5#

#"since these calculations are approximate she should"#
#"probably purchase a few more, say 55"#

If the central angle is #140^@#, then it means #140^@# of a circle was swept with the diameter of #60# inches:

In this case, our radius is then #"30 in."#, or

#30 cancel"in." xx ("1 ft")/(12 cancel"in.") = "2.5 ft"#

One full circle has #360^@# of arc, so this area is #140/360 xx 100% = 38.bar(8)%# the area of a circle.

This area swept out in the circular garden is

#A_"arc" = pir^2 cdot 140/360#

#= pi (2.5)^2 cdot 140/360 = "7.64 ft"^2#

Thus, if she wants #"7 plants/ft"^2#, then she would buy at least:

#"7 plants"/cancel("ft"^2) xx 7.64 cancel("ft"^2) = "53.5 plants"#

Well... then she would need to buy #color(blue)54# plants to buy whole plants.