The radius of a circle is increased by 50%. What is the percentage increase in t

₹0.0

Question: The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)

Options:

Correct Answer: 100%

Exam Year: 2020

Solution:

If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.

The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)

The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)

Step 1: Identify the original radius of the circle, which we will call 'r'.
Step 2: Calculate the new radius after a 50% increase. The new radius is 1.5 times the original radius, so it is 1.5r.
Step 3: Write the formula for the area of a circle, which is Area = πr².
Step 4: Calculate the original area using the original radius: Original Area = πr².
Step 5: Calculate the new area using the new radius: New Area = π(1.5r)².
Step 6: Simplify the new area: New Area = π(1.5r)² = π(2.25r²) = 2.25πr².
Step 7: Find the increase in area by subtracting the original area from the new area: Increase in Area = New Area - Original Area = 2.25πr² - πr².
Step 8: Simplify the increase in area: Increase in Area = (2.25 - 1)πr² = 1.25πr².
Step 9: Calculate the percentage increase in area: Percentage Increase = (Increase in Area / Original Area) × 100%.
Step 10: Substitute the values: Percentage Increase = (1.25πr² / πr²) × 100% = 1.25 × 100% = 125%.

Percentage Increase – Understanding how to calculate the percentage increase in a quantity, specifically in the context of geometric properties like area.
Area of a Circle – Knowledge of the formula for the area of a circle (A = πr²) and how changes in the radius affect the area.
Scaling Factors – Recognizing how scaling a dimension (radius) affects other dimensions (area) in a non-linear way.