Question

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

Answer 1

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.