To find the area of a hubcap (which is circular), you can use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \( r \) is the radius. Given that the radius of the hubcap is 16 centimeters, we can calculate the exact area as follows:
\[ A = \pi (16^2) = \pi (256) = 256\pi \text{ square centimeters} \]
Next, to find the approximate area, we can use the approximation \( \pi \approx 3.14 \):
\[ A \approx 256 \times 3.14 \approx 804.64 \text{ square centimeters} \]
Now, rounding 804.64 to the hundredths place gives us 804.64. That said, we can consider \( \pi \approx 3.14 \) more accurately as \( \pi \approx 3.14159 \):
\[ A \approx 256 \times 3.14159 \approx 804.25 \text{ square centimeters} \]
So rounded to the hundredths place, it remains approximately 804.25 square centimeters.
Now, let's evaluate the options given:
- Option 1: \( 256\pi \) square centimeters (exact area) - This is correct.
- Option 2: \( 803.84 \) square centimeters (approximate area) - This is not correct based on our calculation; it should be around 804.25.
- Option 3: \( 16\pi \) square centimeters (not applicable since this is not the area) - This is not correct.
- Option 4: \( 60.24 \) square centimeters (not applicable since this is not the area) - This is not correct.
Thus, the only acceptable choice is:
- 256π square centimeters (exact area)
The approximate area isn't exactly listed, so none of the approximate values match either.