Question

will medal

Answer 1

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 2

we can start off by finding the radius and side length of the circle and square, respectively

Answer 3

Square:
s^2=36 so s=6

Circle: A=pi*r^2
36=pi*r^2
so r=sqrt(36/pi)=6/√pi

Answer 4

now we can calculate the distance that the circle is sticking out from the square. This distance is simply the diameter of the circle-side length of the square

Answer 5

so the diameter would be would be 2*r= 12/√pi
12/√pi-6 is the "sticking out" distance of the circle

Answer 6

We actually have to multiply this by 2 as there are four places where it sticks out and the diameter only accounts for 2, so it is 24/√pi-12

Answer 7

To find the total sticking out distance of the square, we have to use the "diameter" of the square

Answer 8

we know that both sides are 6, so by the pythagorean theorem, the diameter, or diagonal, is √(6^2+6^2), which comes out to 6√2

Answer 9

now we can subtract the diameter of the circle to get half of the total sticking out distance
6√2-12/√pi,
which we multiply by 2 to get the total
2*(6√2-12/√pi)= 12√2-24/√pi

Answer 10

we can compare the two values 12√2-24/√pi and 24/√pi-12 to see which one is larger.
If i did my calculations right, the first is 3.43 and the second is 1.54, leading the square to have more distance sticking out