MODELING REAL LIFE The diameter of a coaster is 7 centimeters. What is the total area of five coasters? Round to the nearest hundredth if necessary. total area: about \( \square \mathrm{cm}^{2} \)

To find the total area of five coasters, we first need to calculate the area of one coaster and then multiply that by five. 1. **Calculate the radius of one coaster:** The diameter of the coaster is given as 7 cm. The radius \( r \) is half of the diameter: \[ r = \frac{d}{2} = \frac{7}{2} = 3.5 \text{ cm} \] 2. **Calculate the area of one coaster:** The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] Substituting the radius we found: \[ A = \pi (3.5)^2 \] 3. **Calculate the area of five coasters:** The total area for five coasters is: \[ \text{Total Area} = 5 \times A \] Now, let's perform the calculations. First, we will calculate the area of one coaster and then multiply by five. I'll calculate this now. Calculate the value by following steps: - step0: Calculate: \(5\pi \times 3.5^{2}\) - step1: Convert the expressions: \(5\pi \left(\frac{7}{2}\right)^{2}\) - step2: Multiply the terms: \(\frac{245}{4}\pi \) - step3: Multiply: \(\frac{245\pi }{4}\) The area of one coaster is approximately \( 192.42 \, \text{cm}^2 \) when rounded to the nearest hundredth. Thus, the total area of five coasters is: \[ \text{Total Area} \approx 192.42 \, \text{cm}^2 \] So, the final answer is: \[ \text{Total area: about } 192.42 \, \text{cm}^2 \]