Question

You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of each bed.

Answer 1

Radius of larger flower bed = 10 feet

Radius of smaller flower bed = 6 feet

Explanation:

Complete question:

"You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of each bed."

Radius of larger flower bed = r

Radius of smaller flower bed = r - 4

Now,

Area of circle is
`\pi r^2`

Since, total area is
`136\pi`, we can write:

`\pi r^2 + \pi (r-4)^2=136\pi`

Expanding and solving for r:

`\pi r^2 + \pi (r-4)^2=136\pi\\r^2+(r-4)^2=136\\r^2 + r^2 - 8r + 16 = 136\\2r^2-8r-120=0\\2(r+6)(r-10)=0\\r=-6,10`

Radius cannot be negative, so r = 10 & r-4 = 10 -4 = 6

Radius of larger flower bed = 10 feet

Radius of smaller flower bed = 6 feet