Omar has a circular table with a diameter of 10 in, and Mei has a square table with each side measuring 10 in. Omar says that his table will require more material to cover, but Mei disagrees and thinks her table will require more material. Who is correct and why?
Mei, because her table requires 100 in squared of material.
Mei's square table has an area of 100 square inches, calculated by multiplying the length of one side by itself (10 in x 10 in). This area exceeds the area of Omar's circular table, which is smaller and requires less material to cover.
This choice incorrectly states the area of Mei's table. The area of a square table is determined by squaring the length of one side, which in this case is 10 in. Thus, the correct area is 100 square inches, not 40 square inches.
This is the correct answer, as the area of Mei's square table is indeed 100 square inches (10 in x 10 in). This area indicates the amount of material needed to cover her table, making it larger than Omar's circular table.
This choice provides an incorrect area for Omar's table. The area of a circle is calculated using the formula A = πr². With a diameter of 10 in, the radius is 5 in, leading to an area of approximately 78.54 square inches (π x 5²), not 314.16 square inches.
This option also miscalculates the area of Omar's circular table. Using the radius of 5 in, the area is approximately 78.54 square inches. Therefore, the area stated here is significantly less than the actual area required to cover Omar's table.
The comparison of the areas of Omar and Mei's tables shows that Mei's square table, with an area of 100 square inches, requires more material than Omar's circular table, which has an area of approximately 78.54 square inches. Thus, Mei is correct in asserting her table needs more material to cover it, clarifying the misunderstanding between the two regarding the area calculations.
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