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

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Question: If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)

Options:

Correct Answer: Decreases by 25.12 cm²

Exam Year: 2020

Solution:

Area change = π[(r-2)² - r²] = π[-4r + 4] = 3.14 * (-4r + 4).

If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)

If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)

Step 1: Understand that the area of a circle is calculated using the formula A = πr², where r is the radius.
Step 2: Identify the original radius of the circle as 'r'.
Step 3: Calculate the area of the original circle using the formula: A_original = πr².
Step 4: Determine the new radius after decreasing it by 2 cm: new radius = r - 2.
Step 5: Calculate the area of the new circle using the new radius: A_new = π(new radius)² = π(r - 2)².
Step 6: Expand the formula for the new area: A_new = π[(r - 2)(r - 2)] = π[r² - 4r + 4].
Step 7: Now, find the change in area by subtracting the original area from the new area: Area change = A_new - A_original.
Step 8: Substitute the areas: Area change = π[r² - 4r + 4] - πr².
Step 9: Simplify the expression: Area change = π[-4r + 4].
Step 10: Finally, substitute π = 3.14 to find the numerical change in area: Area change = 3.14 * (-4r + 4).

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.
Algebraic Manipulation – Ability to manipulate algebraic expressions to find the difference in areas before and after the radius change.
Substitution and Evaluation – Using specific values (like π = 3.14) to evaluate the final expression for area change.