A parade includes a large spherical balloon. What is the capacity, in US gallons, of the balloon if it has a radius of 24 feet? (There are 7.48 US gallons in a cubic foot.)
A 433 135 US gal
B 476 449 US gal
D 519 762 US gal
C 346 508 US gal
The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.
Substituting the given radius of 24 feet into the formula:
V = (4/3)π(24)^3
V = (4/3)π(13824)
V ≈ 18339.79 cubic feet
To convert cubic feet to US gallons, we can use the conversion factor of 7.48 US gallons per cubic foot.
Capacity in US gallons = 18339.79 cubic feet * 7.48 US gallons per cubic foot
Capacity in US gallons ≈ 136927.57 US gallons
Rounding to the nearest hundred, the capacity of the balloon is approximately 137,000 US gallons.
Therefore, the correct answer is A) 433,135 US gallons.