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Exercise 15.2 1. Find the area of circle with the given radii. \( \begin{array}{lll}\text { (i) } 3 \mathrm{~cm} & \text { (ii) } 7 \mathrm{~cm} & \text { (iii) } 14 \mathrm{~cm}\end{array} \)

Ask by Henry Sanders. in India
Feb 24,2025

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Answer

The areas of the circles are: - (i) 9π cm² - (ii) 49π cm² - (iii) 196π cm²

Solution

To find the area of a circle, use the formula:   Area = π × (radius)² (i) For a radius of 3 cm:   Area = π × (3 cm)² = π × 9 = 9π cm² (ii) For a radius of 7 cm:   Area = π × (7 cm)² = π × 49 = 49π cm² (iii) For a radius of 14 cm:   Area = π × (14 cm)² = π × 196 = 196π cm² Therefore, the areas of the circles are:   (i) 9π cm², (ii) 49π cm², (iii) 196π cm².

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To find the area of a circle, you can use the formula \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. For the given radii: (i) For a radius of \( 3 \, \text{cm} \): \[ A = \pi (3)^2 = 9\pi \, \text{cm}^2 \approx 28.27 \, \text{cm}^2. \] (ii) For a radius of \( 7 \, \text{cm} \): \[ A = \pi (7)^2 = 49\pi \, \text{cm}^2 \approx 153.94 \, \text{cm}^2. \] (iii) For a radius of \( 14 \, \text{cm} \): \[ A = \pi (14)^2 = 196\pi \, \text{cm}^2 \approx 615.75 \, \text{cm}^2. \] So you have approximate areas of \( 28.27 \, \text{cm}^2 \), \( 153.94 \, \text{cm}^2 \), and \( 615.75 \, \text{cm}^2 \) for the circles with radii 3 cm, 7 cm, and 14 cm, respectively!

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