Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

Video Summary

A 30cm square is divided into 9 smaller squares and contains three circles with radii of 5cm, 4cm, and 3cm. The problem leverages Pythagorean triples and notes that the sum area of the two smaller circles (with radii 4cm and 3cm) matches the area of the largest circle (5cm). The combined area of these two smaller circles equals the large circle's area, demonstrating a neat fit. Given the square's side length is 30, with 5 out of 9 squares shaded, the total shaded area is calculated as \( \frac{5}{9} \times 30^2 = 500 \). The correct answer is option B.

Keywords

geometry

Pythagorean triples

circle area

square division

shaded area