# HOT AIR BALLOONS

Date of the Problem
November 27, 2023

Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.

The formula for the volume of a sphere is (4/3) × π × r3. Since we know the diameter of the balloon is 100 feet and the radius r is half the diameter, it follows that the radius is 50 feet. Substituting, we see that, completely filled, Melrose’s balloon will hold (4/3) × π × (50)3 = 523,598.8 ft3 of air.

Coco takes a hot air balloon trip over part of the Alleghany Mountains with her dad. They travel at an average speed of 40 mi/h for 120 miles before they land to take a 45-minute lunch break. After lunch, they fly 175 miles at an average speed of 35 mi/h. Including the lunch break, how many hours was their entire trip? Express your answer as a decimal to the nearest hundredth.

To solve this problem, we will be using the equation distance = rate × time. We’ll let T1 be the number of hours it took them to travel 120 miles at an average speed of 40 mi/h. So, we have 120 = 40T1 → T1 = 120/40 = 3 hours. We’ll let T2 be the number of hours it took them to travel 175 miles at an average speed of 35 mi/h. So, we have 175 = 35T2 → T2 = 5 hours. The lunch break was 45 minutes = 45/60 = 0.75 hours. Therefore, the entire trip, including the lunch break, took 3 + 0.75 + 5 = 8.75 hours.

Rhonda found that 10 super-sized helium balloons provide just enough lift to carry her 3-pound toy. At that same rate, how many super-sized balloons would be required to carry Rhonda’s 81-pound Alaskan malamute?

If 10 balloons lift exactly 3 pounds, then each balloon lifts the equivalent of 3/10 pound. Dividing 81 pounds by 3/10 pound, we see that the number of balloons required to lift her dog is 81/(3/10) = 81 × 10/3 = 810/3 = 270 balloons.

Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.

Page 2 contains ONLY PROBLEMS. ♦

Math topic
CCSS (Common Core State Standard)
Difficulty