Question

Geometry B Final Exam

Ross will make a water balloon that can be modeled with a sphere. A constraint he must consider is that when the radius of the balloon exceeds 5 inches, the balloon will pop. If he uses a garden hose with a flow rate of 12 gallons per minute to fill up the balloon, for how many seconds can he fill it before it pops? Round to the nearest tenth of a second. (1 gallon = 231 cubic inches)


Enter your answer in the box.


___seconds

Not 0. 38

Answer 1

Answer:Ross can fill the balloon for 0.2 seconds before it pops.

Explanation:

Sure thing! Let's calculate the answer to your math problem. The formula to calculate the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since we know that the maximum radius of the balloon is 5 inches, we can calculate the maximum volume of the balloon, which is V = (4/3)π(5)^3 = 523.6 cubic inches.

Now, we need to calculate the time it takes to fill up 523.6 cubic inches of water using a garden hose with a flow rate of 12 gallons per minute. First, we need to convert the volume to gallons, which is 523.6/231 = 2.265 gallons.

Next, we can use the formula: time = volume / flow rate. Plugging in the values, we get time = 2.265 / 12 = 0.189 seconds. Rounded to the nearest tenth of a second, Ross can fill the balloon for 0.2 seconds before it pops. I hope that helps!