A hubcap has a radius of 16 Centimeters. What is the area of the hubcap? Find the exact and approximate (round to hundredths place) answers.

Select all that apply.

Question 7 options:

256π
square centimeters

803.84 square centimeters

16π
square centimeters

60.24 square centimeters

1 answer

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.