How do you calculate the area of a sector with radius 5 cm and angle 90°?

The area of a sector with radius 5 cm and angle 90° is 6.25π cm².

To calculate the area of a sector, you need to know the radius of the circle and the angle of the sector. The formula for the area of a sector is:

\[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \]

where \(\theta\) is the angle in degrees and \(r\) is the radius of the circle.

In this case, the radius \(r\) is 5 cm and the angle \(\theta\) is 90°. Plugging these values into the formula, we get:

\[ \text{Area} = \frac{90}{360} \times \pi \times (5)^2 \]

First, simplify the fraction \(\frac{90}{360}\):

\[ \frac{90}{360} = \frac{1}{4} \]

Next, calculate \(5^2\):

\[ 5^2 = 25 \]

Now, multiply these values together:

\[ \text{Area} = \frac{1}{4} \times \pi \times 25 \]

\[ \text{Area} = \frac{25}{4} \times \pi \]

\[ \text{Area} = 6.25\pi \]

So, the area of the sector is \(6.25\pi\) cm². If you need a numerical value, you can approximate \(\pi\) as 3.14:

\[ 6.25 \times 3.14 \approx 19.625 \]

Therefore, the area of the sector is approximately 19.625 cm².