What is the area of a 7 inch circle?
Understand the Problem
The question is asking for the area of a circle with a radius of 7 inches. To solve this, we will use the formula for the area of a circle, which is A = πr², where r is the radius.
Answer
The area of the circle is $49\pi$ square inches, or approximately 153.86 square inches.
Answer for screen readers
The area of the circle is $49\pi$ square inches, or approximately 153.86 square inches.
Steps to Solve
-
Identify the radius
The radius of the circle is given as 7 inches. We will use this value in our area formula. -
Use the area formula for a circle
The formula for the area of a circle is $A = \pi r^2$. We will substitute the radius into this formula. -
Substitute the radius into the formula
Now we plug in the value of the radius: $$ A = \pi (7)^2 $$ -
Calculate $7^2$
We calculate the square of 7: $$ 7^2 = 49 $$ -
Multiply by π
Now, we can find the area by multiplying 49 by $\pi$: $$ A = 49\pi $$ -
Final calculation (using π ≈ 3.14)
If needed, we can approximate the area using $\pi \approx 3.14$: $$ A \approx 49 \times 3.14 = 153.86 \text{ square inches} $$
The area of the circle is $49\pi$ square inches, or approximately 153.86 square inches.
More Information
The area of a circle is a fundamental concept in geometry, emphasizing how the size of a circle relates to its radius. Understanding this relationship helps in various real-life applications, from measuring physical areas to design and architecture.
Tips
- Forgetting to square the radius: Always remember to apply the exponent to the radius before multiplying by $\pi$.
- Confusing diameter and radius: Ensure you're using the correct measure; the radius is half the diameter.
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