Find the area. Leave it in terms of π.
Understand the Problem
The question is asking to find the area of a circle with a radius of 9 inches and to express the answer in terms of π.
Answer
The area is \( 81\pi \) square inches.
Answer for screen readers
The area of the circle is ( 81\pi ) square inches.
Steps to Solve
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Identify the formula for the area of a circle
The formula to find the area ( A ) of a circle is given by:
$$ A = \pi r^2 $$
where ( r ) is the radius of the circle. -
Substitute the given radius into the formula
Here, the radius ( r ) is 9 inches. Plugging this value into the formula, we get:
$$ A = \pi (9)^2 $$ -
Calculate the squared radius
Now compute ( 9^2 ):
$$ 9^2 = 81 $$ -
Write the final area in terms of ( \pi )
Now, substituting back, we have:
$$ A = 81\pi $$
The area of the circle is ( 81\pi ) square inches.
More Information
The area of a circle grows with the square of its radius. This means even a small increase in radius results in a significantly larger area. Using ( \pi ) allows us to express the area precisely without needing a decimal approximation.
Tips
- Failing to square the radius: Remember to calculate ( r^2 ) before multiplying by ( \pi ).
- Confusing diameter and radius: Make sure to use the radius, which is half of the diameter.
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