To find the area of the top of each drum, we start by using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the drum, and [tex]\( \pi \)[/tex] is approximately 3.14159.
### Step-by-Step Solution:
1. Convert the diameters to radii:
- For a diameter of 10 inches, the radius [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.
- For a diameter of 12 inches, the radius [tex]\( r = \frac{12}{2} = 6 \)[/tex] inches.
- For a diameter of 14 inches, the radius [tex]\( r = \frac{14}{2} = 7 \)[/tex] inches.
2. Calculate the area for each radius:
- For the radius of 5 inches:
[tex]\[ A = \pi \times 5^2 = \pi \times 25 \approx 3.14159 \times 25 \approx 78.5 \text{ square inches} \][/tex]
- For the radius of 6 inches:
[tex]\[ A = \pi \times 6^2 = \pi \times 36 \approx 3.14159 \times 36 \approx 113.1 \text{ square inches} \][/tex]
- For the radius of 7 inches:
[tex]\[ A = \pi \times 7^2 = \pi \times 49 \approx 3.14159 \times 49 \approx 153.9 \text{ square inches} \][/tex]
3. Summarize the results:
- The area of the top of the drum with diameter 10 inches is approximately 78.5 square inches.
- The area of the top of the drum with diameter 12 inches is approximately 113.1 square inches.
- The area of the top of the drum with diameter 14 inches is approximately 153.9 square inches.
The correct answer is:
b. 78.5 Sq in, 113.1 sq in, 153.9 sq in
