Question

4. Mr. Grayson has a circular table made out of wood. The top of this table has an area of 36 ft2. Mr. Grayson asks his assistant to put a square glass piece with an area of 36 ft2 on top of the table. He notices that when the glass is put over the circular table base, the glass sticks out a bit from the base of the table. He says, “The glass is sticking out too far past the edge of the wood.” His assistant says, “The wood actually sticks out from the edge of the glass more than the glass sticks out from the edge of the wood.” Is the assistant correct? What is the distance that each is sticking out from the other? Show your work. Use 3.14 for pi and round to the nearest tenth.

Answer 1

Given:
Area of the circle : 36 ft²
Area of the square : 3 6ft²

Circle:
A = π r²
36 ft² = 3.14 * r²
36 ft² / 3.14 = r²
 11.46 = r²
√11.46 = r
3.39 = r                diameter = 2 * r = 2 * 3.39 = 6.78 ft

Square:
A = a²
36 ft² = a²
√36 ft² = a
6 ft = a

6.78 ft - 6 ft = 0.78 ft ⇒ the table is sticking out from the glass

Diagonal of a square:
d = √ 6² + 6²
d = √ 36 + 36
d = √ 72
d = 8.49 ft

8.49 ft - 6.78 ft = 1.71 ft ⇒ the glass is sticking out from the table