Question: Megan loves to plant sunflowers and plans to fill one of the containers below with soil. The dimensions of each container are shown below.
Container A
$r$
$h=2.5$ ft
$r=1.5$ ft
Container B
$h=3.5$ ft
$w=2$ ft
$l=2$ ft
Container C
$r$
$h=1.5$ ft
$r=2$ ft
Which container holds the largest amount of soil?
1. **State the problem:** We need to find which container holds the largest volume of soil.
2. **Identify container shapes and formulas:**
- Container A and C are cylinders. Volume of a cylinder is given by $$V=\pi r^2 h$$
- Container B is a rectangular prism. Volume of a rectangular prism is $$V=lwh$$
3. **Calculate volume of Container A:**
$$V_A=\pi (1.5)^2 (2.5) = \pi \times 2.25 \times 2.5 = \pi \times 5.625$$
4. **Calculate volume of Container B:**
$$V_B=2 \times 2 \times 3.5 = 4 \times 3.5 = 14$$
5. **Calculate volume of Container C:**
$$V_C=\pi (2)^2 (1.5) = \pi \times 4 \times 1.5 = \pi \times 6$$
6. **Approximate volumes using $\pi \approx 3.1416$:**
- $$V_A \approx 3.1416 \times 5.625 = 17.67$$
- $$V_B = 14$$
- $$V_C \approx 3.1416 \times 6 = 18.85$$
7. **Compare volumes:**
- Container A: $17.67$ cubic feet
- Container B: $14$ cubic feet
- Container C: $18.85$ cubic feet
8. **Conclusion:** Container C holds the largest amount of soil.
**Final answer:** Container C holds the largest volume of soil.