Question

the radius of a sphere - shaped balloon increases at a rate of 2 centimeters (cm) per second. if the surface area of the completely inflated balloon is (784pispace cm^{2}), how long will it take for the balloon to fully inflate? use (sa = 4pi r^{2}) 7 seconds 49 seconds 196 seconds 10 seconds

Explanation:

Step1: Solve for full radius $r$

Set surface area equal to formula:
$$784\pi = 4\pi r^2$$
Divide both sides by $4\pi$:
$$\frac{784\pi}{4\pi} = r^2$$
$$196 = r^2$$
Take square root:
$$r = \sqrt{196} = 14 \text{ cm}$$

Step2: Calculate inflation time

Time = $\frac{\text{Final radius}}{\text{Rate of increase}}$
$$\text{Time} = \frac{14}{2} = 7 \text{ seconds}$$

Answer:

7 seconds