Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To solve for the area of a circle with a given diameter of 16 feet, we need to follow these steps:
1. Determine the radius of the circle:
The radius is half of the diameter.
Since the diameter is 16 feet, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = \frac{16}{2} = 8 \text{ feet} \][/tex]
2. Use the formula for the area of a circle:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the value of the radius [tex]\( r = 8 \)[/tex] feet, we get:
[tex]\[ A = \pi (8)^2 \][/tex]
3. Simplify the expression:
Calculating [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Thus, the area is:
[tex]\[ A = 64 \pi \, \text{square feet} \][/tex]
4. Match this result with the given options to find the correct expression for the area:
- Option A: [tex]\( 8^2 \cdot \pi \)[/tex]
- Option B: [tex]\( 16 \cdot \pi \)[/tex]
- Option C: [tex]\( 16^2 \cdot \pi \)[/tex]
- Option D: [tex]\( 8 \cdot \pi \)[/tex]
We see that Option A matches our expression [tex]\( 8^2 \cdot \pi \)[/tex], which simplifies to [tex]\( 64 \pi \)[/tex].
Therefore, the expression that gives the area of the circle is:
[tex]\[ \boxed{8^2 \cdot \pi} \][/tex]
1. Determine the radius of the circle:
The radius is half of the diameter.
Since the diameter is 16 feet, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = \frac{16}{2} = 8 \text{ feet} \][/tex]
2. Use the formula for the area of a circle:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the value of the radius [tex]\( r = 8 \)[/tex] feet, we get:
[tex]\[ A = \pi (8)^2 \][/tex]
3. Simplify the expression:
Calculating [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Thus, the area is:
[tex]\[ A = 64 \pi \, \text{square feet} \][/tex]
4. Match this result with the given options to find the correct expression for the area:
- Option A: [tex]\( 8^2 \cdot \pi \)[/tex]
- Option B: [tex]\( 16 \cdot \pi \)[/tex]
- Option C: [tex]\( 16^2 \cdot \pi \)[/tex]
- Option D: [tex]\( 8 \cdot \pi \)[/tex]
We see that Option A matches our expression [tex]\( 8^2 \cdot \pi \)[/tex], which simplifies to [tex]\( 64 \pi \)[/tex].
Therefore, the expression that gives the area of the circle is:
[tex]\[ \boxed{8^2 \cdot \pi} \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.