Grades 5-6 Video Solutions 2023-2023_1-2

Video Transcription

Question 10. Jacob glued the three pieces of paper shown onto the black circle on the right.  Which of the following patterns could he not obtain?  The main thing to recognize in this question is that we cannot cut the shapes in any way.  We have to place a half circle and two quarter circles on top of the full circle.  One shape in our answer stands out, C. When we look at it, it is apparent that the gray half circle actually takes up a larger area than just half, because if we had half a circle here, it would cover this area, leaving an extra gray sliver which Jacob does not have. So the answer will be C.

Video Summary

The problem involves arranging a half circle and two quarter circles on a full circle without cutting them. The task is to identify which pattern cannot be created with these shapes. The key observation is that option C features a gray half circle that occupies more than half the area of the circle, suggesting an additional gray area that isn't available. Thus, option C cannot be formed using the given pieces, making it the correct answer.

Keywords

geometry

circle arrangement

half circle

quarter circle

pattern identification