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.
for the first star thing i got
a=3.14 x s^2+81
but i don't understand the other 2 bullets
If your question is so urgent, what have you done to try to solve these problems?
* area of a circle is r^2 times pi
r=9s so r^2 is 9s^2. Multiply this by 3.14 to get the area of the circle. You can't actually solve it with a number since there is a variable involved.
* Area of a square is length times width
* If s=1, the area of the circle is 9^2 x 3.14. Take this answer and subtract it from the area of your square.
Hope this helps. Good luck!
To find the expressions for the area of the larger circle and the area of the square outside the circle, we need to understand the relationship between the given dimensions and the circles.
Let's start by visualizing the situation:
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In the diagram above:
- The square has sides measuring 38 feet.
- The smaller circle has a radius of "s" feet.
- The larger circle has a radius of 9 feet longer than the radius of the smaller circle, i.e., "s + 9".
Now, let's find the expressions for the area of each component:
1. Expression for the area of the larger circle:
The formula for the area of a circle is given by: A = π * r^2, where "A" represents the area, and "r" represents the radius.
For the larger circle, the radius is "s + 9". Therefore, the expression for its area is:
Area of the larger circle = π * (s + 9)^2
2. Expression for the area of the square outside the circle:
The area of the square can be calculated by finding the difference between the total area of the square and the area of the smaller circle.
The area of the square with side length 38 feet is given by: Area of the square = side^2.
Therefore, the expression for the area of the square outside the circle can be written as:
Area of the square outside the circle = (38)^2 - π * s^2
Now, let's use the expressions to find the area when "s = 1":
1. Area of the larger circle (when s = 1):
Area of the larger circle = π * (1 + 9)^2
= π * (10^2)
= π * 100
≈ 314.16 square feet (rounded to two decimal places)
2. Area of the square outside the circle (when s = 1):
Area of the square outside the circle = (38)^2 - π * (1)^2
= 1444 - π
≈ 1176.86 square feet (rounded to two decimal places)
Therefore, when "s = 1", the area of the larger circle is approximately 314.16 square feet, and the area of the square outside the circle is approximately 1176.86 square feet.