Question

1. when you are out fishing, you notice that every time you throw your line in, a circular ripple is produced. what is the spread of the circular ripple after 30 seconds if the ripple travels outward at a speed of 60 cm/s?

the spread of the circular ripple after 30 seconds is 3,600,897.5 cm²?
the spread of the circular ripple after 30 seconds is 13,178,632.9 cm²?
the spread of the circular ripple after 30 seconds is 900.87 cm².
the spread of the circular ripple after 30 seconds is 10,178,751.6 cm²?

Explanation:

Step1: Calculate the radius

Given the speed of the ripple is 60 cm/s (inferred from the partial text "speed of 60") and time \( t = 30 \) s. Using the formula \( \text{distance}=\text{speed}\times\text{time} \), the radius \( r \) of the circular ripple is \( r = 60\times30=1800 \) cm.

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A = \pi r^{2} \). Substitute \( r = 1800 \) cm into the formula: \( A=\pi\times(1800)^{2}=\pi\times 3240000\approx 3.14159\times3240000 = 10178751.6 \) cm².

Answer:

The spread of the circular ripple after 30 seconds is 10,178,751.6 cm² (assuming the speed is 60 cm/s, radius \( r = 60\times30 = 1800 \) cm, area \( A=\pi r^{2}=\pi\times1800^{2}\approx 10178751.6 \) cm²)