Question

A hose is dripping water slowly onto the ground and forming a growing circular puddle. Approximate the change in the area of the puddle from the time when the radius is 3 cm to the time when the radius of the puddle is 3.40 cm. All answers are given in square centimeters.

a) 12.56 cm²
b) 7.84 cm²
c) 19.63 cm²
d) 15.72 cm²

Answer 1

The change in area of the puddle as its radius increases from 3 cm to 3.40 cm is approximately 8.03 cm², but the closest answer option provided is b) 7.84 cm².

Step-by-step explanation:

To approximate the change in the area of a growing circular puddle as its radius increases, we can use the formula for the area of a circle, A = πr², where A is the area and r is the radius. When the radius is 3 cm, the area is A1 = π * (3 cm)². When the radius is 3.40 cm, the area is A2 = π * (3.40 cm)². The change in area is given by the difference, ΔA = A2 - A1.

Calculations:

• A1 = π * (3 cm)² = 28.26 cm²
• A2 = π * (3.40 cm)² = 36.29 cm²
• ΔA = 36.29 cm² - 28.26 cm² = 8.03 cm²

The correct answer, which is closest to our calculated change in area, would be option b) 7.84 cm²; however, please note that there has been a minor calculation mistake, as the actual calculated change is 8.03 cm².