Question

At a campground a rectangular fire pit is 4 feet by 3 feet what is the area of the largest Circular fire that can be made in this fire pit use 3.14 for pi round to the nearest square inch

Answer 1

The area of the largest circular fire pit will be 19.625 sq ft.

Explanation:

Given,

The length of the rectangular pit (L) = 4 ft

The width of the rectangular pit (B) = 3 ft

To find the area of the largest circle we need to find the diagonal of the rectangle first.

The diagonal will be the diameter of the circle.

Formula

By Pythagoras theorem,
`hypotenuse^(2) = base^(2)+height^(2)`

The area of a circle of radius r is = π
`r^(2)` sq ft

Now the diagonal of the rectangle =
`\sqrt{L^(2) +B^(2) }` ft

=
`\sqrt{4^(2) +3^(2) }` ft

=5 ft

The diameter of the circle is 5 ft

So, the radius = 2.5 ft

The area of the circle = 3.14 ×
`2.5^(2)` sq ft

= 19.625 sq ft