A container is entirely filled with 950,000 gallons of water. How much water is left inside the container if 100 metal spheres, whose radius is 2 m each, are gently placed inside the container? Express your answer in gallons.
V =
Answer
gallons (amount of water left in the container)
Answers
Step-by-step explanation:
V(metal spheres) = 100×(4/3)×π×(2^3)
= 3351.03 cubic m = 3351.03 × 264.72 gallons
= 885242.167 gallons
V(left) = 950000 - 885242.167
= 64757.833 gallons
Volume of water left inside the container = 64,399 gallons.
Step-by-step explanation:
Given: A container is entirely filled with 950,000 gallons of water.
Find: How much water is left inside the container if 100 metal spheres, whose radius is 2 m each, are gently placed inside the container?
Solution:
1 gallon = 3.785 liters
1 cubic meter = 1000 liters
The metal balls will displace an equal volume of water when placed in the container.
Volume of container = 950,000 gallons.
Radius of sphere = 2m
Volume of one sphere = 4/3πr³ = 4/3 * 22/7 * 2 * 2 * 2 = 33.52 cu. m.
Volume of 100 spheres = 33.52 * 100 = 3352 cu.m.
Expressing volume in liters, 3352 cu. m. = 3352 * 1000 liters = 3,352,000 liters.
Expressing volume in gallons, 3,352,000 liters = 3,352,000 / 3.785 = 885,601 gallons.
Volume of water left inside the container = 950,000 - 885,601 = 64,399 gallons.