a high school wrestling mat must be square with 38-foot sides and contain two circles as shown. suppose the inner circle has a radius of "s" feet and the outer circle's radius is nine feet longer than the inner circle.
*write an expression for the area of the larger circle.
* write an expression for the area of the suqare outside the circle.
*use the expression to find the area if s=1.
Does anyone know the answers for this one?
The radius of a circle is 98 mm. What is the area of the circle? Write your answer to the hundredths place. Use 3.14 for π.
The area of the circle is given by the formula A = πr^2, where r is the radius of the circle.
Substituting the given values, we get:
A = 3.14 x (98)^2
A = 30171.52
Rounding to two decimal places, the area of the circle is 30171.52 mm^2.
How come I get different answers?
It's possible that you made a mistake in your calculations or used a different value for pi.
Using the correct value of pi, the area of the circle with radius 98 mm should be:
A = πr^2
A = 3.14 x (98)^2
A = 30171.52 mm^2
If you used a different value for pi, your answer would be different. For example, if you used 3.14159 for pi, your answer would be:
A = πr^2
A = 3.14159 x (98)^2
A = 30194.03 mm^2
However, since the question specifies to use 3.14 for pi, you should use that value to get the correct answer.
To find the area of the larger circle, we need to write an expression using the radius of the inner circle, which is "s."
The radius of the outer circle is nine feet longer than the inner circle, so the radius of the outer circle can be represented as "s + 9."
The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius.
Hence, the expression for the area of the larger circle is A_outer = π(s + 9)^2.
Next, let's write the expression for the area of the square outside the circle.
The sides of the square are given as 38 feet. Since all four sides of a square are of equal length, the length of each side is 38 feet. Therefore, the formula to find the area of a square is A = side^2.
Hence, the expression for the area of the square outside the circle is A_square = 38^2.
Now, let's find the area if s = 1.
To find the area of the larger circle, substitute s = 1 into the expression we derived earlier:
A_outer = π(1 + 9)^2 = π(10)^2 = 100π (square feet)
To find the area of the square outside the circle:
A_square = 38^2 = 1444 (square feet)
Therefore, when s = 1, the area of the larger circle is 100π square feet, and the area of the square outside the circle is 1444 square feet.