Question

Question #ef5d9

Answer 1

`~~54`

Explanation:

`"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"`

Answer 2

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.