Question

a circular garden is enlarged so that the new diameter is twice the old diameter. what is the ratio of the original area to the enlarged area? express your answer as a common fraction.

Answer 1

The ratio of original area to enlarged area is 1/4.

Explanation:

Area of original circular garden is

`\pi {( (d)/(2) )}^(2) = \pi \frac{ {d}^(2) }{4}`

Area of enlarged circular garden is

`\pi ( { (2d)/(2)) }^(2) = \pi {d}^(2)`

So the ratio of original area to enlarged area is 1/4.