To find the area of a quarter circle with a radius of 16 centimeters, we'll follow these steps:
1. Determine the formula for the area of a full circle:
The formula for the area [tex]\( A \)[/tex] of a full circle with radius [tex]\( r \)[/tex] is:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\( \pi \)[/tex] (pi) is approximately 3.14.
2. Calculate the area of the full circle:
Substituting [tex]\( r = 16 \)[/tex] cm into the formula:
[tex]\[
A = 3.14 \times (16)^2
\][/tex]
First, we calculate [tex]\( 16^2 \)[/tex]:
[tex]\[
16^2 = 256
\][/tex]
Then, multiply by [tex]\( \pi \)[/tex]:
[tex]\[
A = 3.14 \times 256
\][/tex]
To find the product:
[tex]\[
3.14 \times 256 = 803.84
\][/tex]
So, the area of the full circle is [tex]\( 803.84 \)[/tex] square centimeters.
3. Find the area of the quarter circle:
A quarter circle is one-fourth of a full circle, so we divide the full circle's area by 4:
[tex]\[
\text{Area of quarter circle} = \frac{A}{4} = \frac{803.84}{4}
\][/tex]
Perform the division:
[tex]\[
\frac{803.84}{4} = 200.96
\][/tex]
4. Round the answer to the nearest hundredth:
The area of the quarter circle, already calculated as 200.96, does not need any further rounding as it is already rounded to the nearest hundredth.
Therefore, the area of the quarter circle is [tex]\( 200.96 \)[/tex] square centimeters.
