Question

the canopy of a parachute is a semicircle with a radius of 13 feet. a company that is making parachutes for a fourth of july celebration wants each parachute to be made from equal parts of red, white, and blue fabric. approximately how much fabric of each color will be needed to make a single parachute canopy?
88.5 ft
88.5 ft²
265.5 ft
265.5 ft²

Explanation:

Step1: Calculate area of semicircle

The formula for the area of a full circle is \( A = \pi r^2 \), so for a semicircle, it's \( A_{semicircle} = \frac{1}{2}\pi r^2 \). Given \( r = 13 \) feet, substitute:
\( A_{semicircle} = \frac{1}{2} \times \pi \times 13^2 \)
\( = \frac{1}{2} \times \pi \times 169 \)
\( \approx \frac{1}{2} \times 3.14 \times 169 \)
\( = 1.57 \times 169 \)
\( \approx 265.33 \, \text{ft}^2 \) (approximate area of the semicircular canopy)

Step2: Divide by 3 (for three colors)

Since the fabric is divided equally into red, white, and blue (3 parts), the area for each color is \( \frac{265.33}{3} \approx 88.44 \, \text{ft}^2 \), which rounds to \( 88.5 \, \text{ft}^2 \).

Answer:

B. \( 88.5 \, \text{ft}^2 \)