SOLUTION: The diagram shows an ancient coin which was used in China. The coin is a circle of 3cm with a square of X Cm removed from its centre . (a) find an expression for the area of one s

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Question 972919: The diagram shows an ancient coin which was used in China. The coin is a circle of 3cm with a square of X Cm removed from its centre .
(a) find an expression for the area of one side of the coin in terms of X and π.
(b) The area of one side of the coin is 7πcm².
Find the area of the square by performing an equation in x.
(Take π to be 3.14)





Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
PART A:
The question is unclear. We will assume X=side of square.
If 3cm=radius of coin:
Area=%28pi%29r%5E2-X%5E2
Area=%28pi%29%289cm%5E2%29-X%5E2
Area=9%28pi%29cm%5E2-X%5E2
.
If 3cm=diameter of coin:
Area=%28pi%29%281.5cm%29%5E2-X%5E2
Area=2.25%28pi%29cm%5E2-X%5E2
.
If 3cm=circumference of coin:
Area=%28pi%29%28C%2F2%28pi%29%29%5E2-X%5E2
Area=%28pi%29%283cm%2F2%28pi%29%29%5E2-X%5E2
Area=%28pi%29%289cm%5E2%2F4%28pi%29%5E2%29-X%5E2
Area=9cm%5E2%2F4%28pi%29-X%5E2
.
PART B:
Since 3cm as radius yields the only workable solution, we will use that as example:
Area=7%28pi%29cm%5E2
.
Area=9%28pi%29cm%5E2-X%5E2
7%28pi%29cm%5E2=9%28pi%29cm%5E2-X%5E2 Subtract 7(pi)cm^2 from each side
0=2%28pi%29cm%5E2-X%5E2 Add X^2 to each side.
X%5E2=2%28pi%29cm%5E2
Since X=side of square, area of square=X%5E2=2%28pi%29cm%5E2