On a certain hot summer day, 413 people used the swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $792.00. How many children and how many adults swam at the public pool that day?

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.