Grades 11-12 Video Solutions 2021-video 2021 11-12/4

Video Transcription

Video Summary

The problem involves a large square divided into smaller squares, each containing an inscribed circle. The task is to determine the proportion of the larger square's area that is shaded by these circles. For one smaller square and its inscribed circle, the circle's radius is \( r \), resulting in an area of \( \pi r^2 \). The square's side is \( 2r \), making its area \( (2r)^2 = 4r^2 \). Thus, the ratio of the circle's area to the square's area is \( \pi/4 \). Since this ratio applies to all smaller squares and circles, the proportion of the shaded area in the larger square is also \( \pi/4 \).

Keywords

geometry

proportion

inscribed circles

area ratio

shaded area