Question
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Follow the steps to find the area of the shaded region. First, use the formula below to find the area of the whole sector. Sector Area \( = \) \[ \left(\frac{\text { angle of sector }}{360}\right) \pi r^{2} \] Sector Area \( =[?] \mathrm{cm}^{2} \) Round to four decimal places

Ask by Vega John. in the United States
Jan 29,2025

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Tutor-Verified Answer

Answer

To find the area of the shaded region, use the sector area formula: \[ \text{Sector Area} = \left(\frac{\text{angle of sector}}{360}\right) \times \pi r^{2} \] Provide the radius and central angle to calculate the area.

Solution

Sure, I'd be happy to help you find the area of the shaded region using the sector area formula. However, I'll need a bit more information to proceed. Specifically, please provide the following details: 1. **Radius (\( r \)) of the sector**: This is the distance from the center of the circle to any point on its circumference. 2. **Central angle (\( \theta \)) of the sector**: This is the angle formed at the center of the circle by the two radii that define the sector. Once you provide these values, we can plug them into the formula and calculate the area of the whole sector. If there are additional steps or details related to the shaded region (such as subtracting areas of other shapes), please include those as well. **Example Calculation:** To illustrate how the calculation works, here's an example. Suppose you have: - **Radius (\( r \))**: 5 cm - **Central angle (\( \theta \))**: 60 degrees **Step 1: Use the Sector Area Formula** \[ \text{Sector Area} = \left(\frac{\theta}{360}\right) \times \pi r^2 \] **Step 2: Plug in the Values** \[ \text{Sector Area} = \left(\frac{60}{360}\right) \times \pi \times (5)^2 \] **Step 3: Perform the Calculation** \[ \text{Sector Area} = \left(\frac{1}{6}\right) \times \pi \times 25 = \frac{25\pi}{6} \approx 13.08997 \, \text{cm}^2 \] **Step 4: Round to Four Decimal Places** \[ \text{Sector Area} \approx 13.0900 \, \text{cm}^2 \] If you provide the specific values for your problem, I can perform the exact calculation for you!

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Bonus Knowledge

To find the area of the shaded region, first identify the angle of the sector and the radius \( r \) of the circle. Let’s say the angle is \( \theta \) degrees and the radius is \( r \) cm. Plug these values into the formula for the sector area, giving you \( \left(\frac{\theta}{360}\right) \pi r^{2} \). Make sure to perform the calculations accurately and round your answer to four decimal places for precision! Once you obtain the sector area, if you need the area of the shaded region specifically, remember to subtract any unwanted areas (like triangles or smaller sectors) from your total sector area to isolate the shaded portion. Always double-check your calculations to avoid any common mistakes, such as not rounding correctly or misinterpreting the angle!

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