Question

area of quarter circles #3
you can find the area of a quarter circle by finding a fourth of the area of the circle. so, you can use the formula ( a=\frac{pi r^{2}}{4} ), where ( r ) is the radius.
directions: find the area of each quarter circle below. use 3.14 for ( pi ). round your answer to the nearest hundredth if needed.
1.
2.
3.
4.
5.
8.

Explanation:

Step1: Substitute the radius into the formula

For problem 1, \(r = 2\) ft. Using the formula \(A=\frac{\pi r^{2}}{4}\), we substitute \(r = 2\) and \(\pi=3.14\).
\(A=\frac{3.14\times2^{2}}{4}\)

Step2: Calculate the value

First, calculate \(2^{2}=4\). Then, \(3.14\times4 = 12.56\). Finally, \(\frac{12.56}{4}=3.14\) \(ft^{2}\).

For problem 2, \(r = 11\) m.
\(A=\frac{3.14\times11^{2}}{4}=\frac{3.14\times121}{4}=\frac{379.94}{4}=94.985\approx94.99\) \(m^{2}\)

For problem 3, \(r = 18\) in.
\(A=\frac{3.14\times18^{2}}{4}=\frac{3.14\times324}{4}=\frac{1017.36}{4}=254.34\) \(in^{2}\)

For problem 4, \(r = 15.6\) cm.
\(A=\frac{3.14\times(15.6)^{2}}{4}=\frac{3.14\times243.36}{4}=\frac{764.1424}{4}=191.0356\approx191.04\) \(cm^{2}\)

For problem 5, \(r = 9.5\) ft.
\(A=\frac{3.14\times(9.5)^{2}}{4}=\frac{3.14\times90.25}{4}=\frac{283.385}{4}=70.84625\approx70.85\) \(ft^{2}\)

For problem 6, \(r = 26.3\) cm.
\(A=\frac{3.14\times(26.3)^{2}}{4}=\frac{3.14\times691.69}{4}=\frac{2171.9066}{4}=542.97665\approx542.98\) \(cm^{2}\)

For problem 7, \(r = 14.2\) in.
\(A=\frac{3.14\times(14.2)^{2}}{4}=\frac{3.14\times201.64}{4}=\frac{633.1496}{4}=158.2874\approx158.29\) \(in^{2}\)

For problem 8, \(r = 28.9\) m.
\(A=\frac{3.14\times(28.9)^{2}}{4}=\frac{3.14\times835.21}{4}=\frac{2622.5594}{4}=655.63985\approx655.64\) \(m^{2}\)

Answer:

1. \(3.14\) \(ft^{2}\)
2. \(94.99\) \(m^{2}\)
3. \(254.34\) \(in^{2}\)
4. \(191.04\) \(cm^{2}\)
5. \(70.85\) \(ft^{2}\)
6. \(542.98\) \(cm^{2}\)
7. \(158.29\) \(in^{2}\)
8. \(655.64\) \(m^{2}\)