Question

The radius of a circle is increased from 10 to 10.06 m. Estimate the resulting change in area.

a) 0.012 m²
b) 0.024 m²
c) 0.048 m²
d) 0.096 m²

Answer 1

The resulting change in area when the radius of a circle is increased from 10 to 10.06 m is approximately 3.983 m².

Step-by-step explanation:

The formula for the area of a circle is A = πr², where π is a constant approximately equal to 3.14159 and r is the radius of the circle.

In this case, the original radius of the circle is 10 m, and the new radius is 10.06 m. To find the change in area, we can subtract the original area from the new area.

Original Area = π(10 m)² = 314.159 m²

New Area = π(10.06 m)² = 318.142 m²

Change in Area = New Area - Original Area = 318.142 m² - 314.159 m² = 3.983 m² (approximately)

Therefore, the resulting change in area is approximately 3.983 m².