# circle problem

• Apr 25th 2010, 10:56 AM
sri340
circle problem
A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter of the garden? Round your answer to the nearest whole number.
• Apr 25th 2010, 12:01 PM
Amer
Quote:

Originally Posted by sri340
A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter of the garden? Round your answer to the nearest whole number.

suppose the garden has the radius "r"

so the area of the walk $= (r+14)^2 \pi - r^2 \pi$
the area of the big circle ( garden with the walk) - the area of the garden

and this equal to the area of the garden

$(r+14)^2 \pi - r^2 \pi = r^2 \pi$

find r and multiply it with 2 , that's the diameter