Math extra credit?

Question

A round table can be made square by dropping the four leaves. If a side of the square table measures 36 inches, to the nearest hundredth of a square inch, how much smaller is the area of the table when the leaves are down than when the leaves are up?

Answer 1

Draw yourself a picture, then you will see that the square table has an area of 36 * 36 and the round table has a diameter of the diagonal of the square or 36 * sqrt(2) from this you can figure the area of the circle.

Don't forget that the question wants the difference in area of the two "tables".

Answer 2

The round table area = pi*(36/2)^2 =1017.88 square inches
the squared table area = 36*36 = 1296 squared inches
the difference = 1296 - 1017.88 = 278.12 squared inches
round it to nearest hundreds of square inches = 300 squared inches

Answer 3

The area of the Square = 36 x 36 = 1296

Since the diagonal cutting through the square is the hypotenuse of the 2 triangles, it is also the diameter of the circle. Hence, we should find the size of the hypotenuse.
Therefore the hypotenuse = side c should be found.
The other two sides are known to us. side a = 36 and side b = 36
The formula to find the hypotenuse is Square root of (a^2+b^2)=c
which is root of (1296+1296) = 50.91169
thus we arrive at the diameter of the circle = 50.91169.
Now the area of the circle is very easy = 3.14XradiusXradius = 2033.78.
The difference between the area of the circle - area of the square = 2033.78 -1296 = 737.78 will be the area lost.

Answer 4

Hey, guess what "extra credit" means.

Seriously, this is way easy. The diameter of the round table equals the length of the diagonal of the square table. Work it out.

Answer 5

I won't give you the answer, but here's some help:

Area of circle = pi * (radius)^2

Area of square = (width)^2

See also Pythagorean theorem: http://en.wikipedia.org/wiki/Pythagorean_theorem

Answer 6

739.75 square inches less.

Answer 7

It is 740.57 sq cm. Need details? Write on @yahoo.com