Math geniuses!! help me out here!?

Question

This is the one problem keeping me from passing trig. PLEASE HELP IF YOU CAN!!

A round table can be made square by dropping the 4 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 then when the leaves are up.

THANKS!

Answer 1

Because each side of the table is 36 inches, that means that the distance from any of the four baselines to center is 18 inches. Now, you have to use the pythagorean theorem to determine the radius of the table The square root of (2(18^2)) equals 25.456 therefore, the table has a radius of 25.456 inches.

So now figure the surface area of the table by taking (pi)(r^2) which equals (3.142)(25.456^2) = 2035.75 square inches.

Now figure the surface area of the table with the leaves down, which is simply 36 squared. This equals 1,296 square inches.

Now take the difference 2035.75 - 1,296 = 739.75 square inches of difference when the leaves are up versus when the leaves are down.

Answer 2

Ok. Let's start with what we know. The square table's area is 36 x 36 which is 1296 square inches. Now, to think about the circular table.

The diameter of the circular table will have the same measurement as the diagonal of the square table. Using the Pythagorean Theorem, we know that the diagonal must be equal to the square root of the sum of the squares of two sides. Or, the diagonal is equal to the square root of 1296+1296 = 2592. This is 50.91168825 or approx. 51 inches.

So, the area of the circle will be pi times the square of the radius or 3.14 x (51/2)^2 = 3.14 x 650.25 = 2041.785 square inches. Now, for the difference.

2041.785 - 1296 = 745.785.

Answer 3

if a side of the square is 36 then the diagonal is 36*sqrt(2), so the radius of the circle is 18*sqrt(2), so the area of the circle is 18^2 * 2 * pi, or 648*pi, and the area of the square is 36^2 or 1296

incidentally 648*pi is like 2035.75

i suppose that sounds possible

Answer 4

area of table when leaves are down = 36 in X 36 in = 1296 sq. in.

diameter of the round table = sq. root of (36 ^2 X 36^2) = 51 in.

radius of the round table = 51 in. / 2 = 25.5 in.

area of table when leaves are up = 3.14 X r ^2 = 3.14 X (25.5)^2 = 2042 sq. in.

difference = 2042 - 1296 = 746 sq. in.

Answer 5

The square has an area of 9 ft^2 right?

The diameter (2*r) of the circle is equal to the diagonal of the square = sqrt(18) ft (pythagorean)

Therefore the area of the circle (pi*r^2) is 9/2 pi. = 14.14 ft^2

The square is 5.14 ft^2 smaller.

Answer 6

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