Home > Math > Detail
search_icon
Question

The fountain at the Palace of Versailles in France is circular in shape. An architect from New York replicates the design of this fountain, but enlarges the radius of the fountain using a scale of 1 : 4. The area of the fountain in New York is 1,600π square yards. What is the area, in square yards, of the original fountain at the Palace of Versailles? Leave your answer in terms of π.

Answer

The area of the fountain situated at the Palace of Versailles was 16π square yards. This was calculated using the fountain's radius on a scale of 1:4. The area of a circle is calculated by multiplying the square of its radius by pi (A=πr², where 'r' represents the radius). In New York, the same fountain on a 1:4 scale has an area of 1,600π square yards. To determine the original fountain's area at the Palace of Versailles, we can establish the ratio A₁:A₂=πr²:π(4r)². By simplifying this ratio, we arrive at A₁=16π square yards. Thus, the original fountain's area was 16π square yards at the Palace of Versailles. To learn more about calculating the area of a circle, please visit brainly.com/question/19794723.