Posted by matt on .
New flowers are being planted in acurcular flower bed with a 14-foot dimeter.if each flower requires 1 square foot of space,about how many flowers can be planted
I would agree - B.
The surface area of a circular flower bed is is pi × r2.That calculates to 153.938 square ft. Rounded to 154. (B).
pi * 7^2 = 154
Not so fast ..... -
Since each flower needs 1 square foot, the flowers planted along the circumference will not have a complete square foot.
To illustrate, take a grid paper, and draw a circle with radius 7.
we will need x^2 + y^2 = 49
you only have to look at 1/4 of the circle and look at the number of entire squares in that quarter circle.
The row on top of the radius can hold only 6 flowers,
so will the 2nd and 3rd row.
But the 4th row can only have 5 squares, or 5 flowers
the 5th row, 4 flowers
the 6th row 3 flowers, but
the 7th row cannot contain any flowers
so the quarter circle can hold 30 flowers
for a total of 120 flowers.
math - back to speed -
Reiny is, of course, correct, but given the choice of answers, I went with the assumption that they were just looking for knowledge of the area of the circle.
And besides, who said that the flower areas were of any particular shape? Nothing says that the plants around the edge can't be in squashy areas!