If the radius of a circle is decreased by 2 cm, how does the area change? (Origi

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Question: If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)

Options:

Correct Answer: Decreases by 25.12 cm²

Exam Year: 2021

Solution:

Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².

If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)

If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)

Step 1: Identify the original radius of the circle, which is 10 cm.
Step 2: Calculate the original area using the formula for the area of a circle: Area = π * (radius)². So, Area = π * (10)².
Step 3: Calculate (10)², which is 100.
Step 4: Multiply 100 by π (approximately 3.14) to find the original area. So, Original Area = 3.14 * 100 = 314 cm².
Step 5: Identify the new radius after decreasing by 2 cm. New radius = 10 cm - 2 cm = 8 cm.
Step 6: Calculate the new area using the same formula: Area = π * (8)².
Step 7: Calculate (8)², which is 64.
Step 8: Multiply 64 by π (approximately 3.14) to find the new area. So, New Area = 3.14 * 64 = 201.06 cm².
Step 9: Find the change in area by subtracting the new area from the original area. Change = Original Area - New Area.
Step 10: Calculate the change: 314 cm² - 201.06 cm² = 112.94 cm².

Area of a Circle – Understanding how to calculate the area of a circle using the formula A = πr² and how changes in the radius affect the area.
Impact of Radius Change – Analyzing how a decrease in radius impacts the overall area, emphasizing the quadratic relationship between radius and area.