Question

How many​ flowers, spaced every 6 ​in., are needed to surround a circular garden with a 100​-ft ​radius?

Please help! URGENT! I appreciate!

Answer 1

See a solution process below:

Explanation:

First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

`C = 2pir`

If we substitute `100"ft"` for `r` and use `3.14` to approximate `pi` we get a circumference of:

`C = 2 * 3.14 * 100"ft"`

`C = 6.28 * 100"ft"`

`C = 628"ft"`

We can now convert the circumference in feet to inches;

`628"ft" xx (12"in")/(1"ft") =>`

`628color(red)(cancel(color(black)("ft"))) xx (12"in")/(1color(red)(cancel(color(black)("ft")))) =>`

`628 xx 12"in" =>`

`7536"in"`

To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:

`7536"in" xx (1" flower")/(6"in") =>`

`7536color(red)(cancel(color(black)("in"))) xx (1" flower")/(6color(red)(cancel(color(black)("in")))) =>`

`7536 xx (1" flower")/6 =>`

`(7536" flower")/6 =>`

`1256" flower"`

You would require 1,256 flowers