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 15 feet. Container B has a diameter of 18
feet and a height of 11 feet. Container A is full of water and the water is pumped into Containe
B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tent
of a cubic foot?

Question

UpStudy AI · Accepted Answer

To determine the volume of water in Container B after pumping all the water from Container A, we'll follow these steps:

### 1. Calculate the Volume of Container A
Container A is a cylinder with:
- **Diameter:** 14 feet ⇒ **Radius (r₁):** 7 feet
- **Height (h₁):** 15 feet

The volume $$ V_A $$ of a cylinder is given by:
$$ V_A = \pi r_1^2 h_1 $$
$$ V_A = \pi (7)^2 (15) $$
$$ V_A = \pi \times 49 \times 15 $$
$$ V_A = 735\pi \, \text{cubic feet} $$

### 2. Calculate the Capacity of Container B
Container B is also a cylinder with:
- **Diameter:** 18 feet ⇒ **Radius (r₂):** 9 feet
- **Height (h₂):** 11 feet

The volume $$ V_B $$ of Container B is:
$$ V_B = \pi r_2^2 h_2 $$
$$ V_B = \pi (9)^2 (11) $$
$$ V_B = \pi \times 81 \times 11 $$
$$ V_B = 891\pi \, \text{cubic feet} $$

### 3. Transfer Water from Container A to Container B
Since Container A holds $$ 735\pi \, \text{cubic feet} $$ of water and Container B can hold up to $$ 891\pi \, \text{cubic feet} $$, Container B has enough capacity to hold all the water from Container A.

### 4. Final Volume in Container B
After transferring all the water:
$$ \text{Volume in Container B} = 735\pi $$

### 5. Calculate the Numerical Value
Using $$ \pi \approx 3.141592653589793 $$:
$$ 735\pi \approx 735 \times 3.141592653589793 $$
$$ 735\pi \approx 2309.0706 \, \text{cubic feet} $$

Rounding to the nearest tenth:
$$ \text{Volume in Container B} \approx 2309.1 \, \text{cubic feet} $$

**Answer:**  
After rounding, Container B holds approximately 2 309.1 cubic feet of water.
After transferring all the water, Container B holds approximately 2,309.1 cubic feet of water.

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