Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 feet and a height of 9 feet. Container B has a diameter of 10 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
Answers
Answer:
The percentage ≅ 48.4%
Step-by-step explanation:
* Lets revise how to find the volume of a container shaped cylinder
- The volume of any container = area of its base × its height
- The base of the cylinder is a circle, area circle = 2 π r,
where r is the length of its radius
* In container A:
∵ r = 13 feet , height = 13 feet
∴ Its volume = π (13)² × (13) = 2197π feet³
* In container B:
∵ r = 9 feet , height = 14 feet
∴ Its volume = π (9)² × (14) = 1134π feet³
* So to fill container B from container A, you will take from
container A a volume of 1134π feet³
- The volume of water left in container A = 2197π - 1134π = 1063π feet³
* To find the percentage of the water that is full after pumping
is complete, divide the volume of water left in container A
by the original volume of the container multiplied by 100
∴ The percentage = (1063π/2197π) × 100 = 48.3841 ≅ 48.4%