Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 13 feet and a height of 13 feet. Container B has a radius of 9 feet and a height of 14 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.

To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?

Answer 1

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%

Answer 2

Using the volume of a cylinder, it is found that 48.4% of Container A is full after the pumping is complete.

What is the volume of a cylinder?

• The volume of a cylinder of radius r and height h is given by:

$V = \pi r^2h$

Volume of Cylinder A

• It has radius of 13 feet and height of 13 feet, hence $r = 13, h = 13$.

Then, its volume, in cubic feet, is:

$V_A = \pi(13^2)(13) = 2197\pi$

Volume of Cylinder B

• It has radius of 9 feet and height of 14 feet, hence $r = 9, h = 14$.

Then, its volume, in cubic feet, is:

$V_B = \pi(9^2)(14) = 1134\pi$

After the pumping is complete

• The volume in container B will be of $1134\pi$ cubic feet.

• In container A, it will be of $2197\pi - 1134\pi = 1063\pi$ cubic feet, out of a total of $2197\pi$.

Hence, the percentage is:

$P = \frac{1063\pi}{2197\pi} \times 100\% = 48.4\%$

48.4% of Container A is full after the pumping is complete.

To learn more about the volume of a cylinder, you can take a look at https://brainly.com/question/9408912