Geometry

Question Analysis

The main focus is using the formula for the area of a circle and the concept of fractions to find the area of the part of the circular bed reserved for roses. First, we need to find the radius from the given diameter, then calculate the total area of the circle, and finally determine the area of the rose - reserved part based on the fraction.

Key Concept Explanation

The area of a circle is calculated by the formula , where  is the radius of the circle. When a fraction of the circle is considered,  the area of that part is found by multiplying the fraction with the total area of the circle. Here, the fraction of the circle reserved for roses is , so the area of the rose - reserved part .

Step - by - Step Solution

1. Find the radius of the circular bed. Given the diameter  feet, the radius  feet.

2. Calculate the total area of the circular bed using the formula . Substitute  into the formula: