A particular brand of talcum powder is available in two packs, a plastic can with a square base of side 5 cm and of height 14 cm, or one with a circular base os rdius 3.5 cm and of height 12 cm. Which of them has greater capacity and by how much?

Answer

To solve the problem, we need to calculate the volumes of both the plastic can with a square base and the circular can, and then compare them to determine which one has a greater capacity and by how much.

### Step-by-Step Solution:

1. **Calculate the Volume of the Plastic Can (Square Base)**:
- The formula for the volume \( V \) of a cuboid (or a can with a square base) is given by:
\[ V = \text{side}^2 \times \text{height} \]
- Here, the side of the square base is 5 cm and the height is 14 cm.
- Substituting the values:
\[ V = 5 \times 5 \times 14 = 25 \times 14 = 350 \, \text{cm}^3 \]

2. **Calculate the Volume of the Circular Can**:
- The formula for the volume \( V \) of a cylinder (circular can) is given by:
\[ V = \pi r^2 h \]
- Here, the radius \( r \) is 3.5 cm and the height \( h \) is 12 cm. We will use \( \pi \approx \frac{22}{7} \).
- First, calculate \( r^2 \):
\[ r^2 = 3.5 \times 3.5 = 12.25 \]
- Now substitute the values into the volume formula:
\[ V = \frac{22}{7} \times 12.25 \times 12 \]
- Simplifying this:
\[ V = \frac{22 \times 12.25 \times 12}{7} \]
- Calculate \( 22 \times 12.25 = 270.5 \):
\[ V = \frac{270.5 \times 12}{7} = \frac{3246}{7} \approx 462 \, \text{cm}^3 \]

3. **Compare the Volumes**:
- Volume of the plastic can = 350 cm³
- Volume of the circular can = 462 cm³
- Since \( 462 > 350 \), the circular can has a greater capacity.

4. **Calculate the Difference in Capacity**:
- To find out by how much the circular can is greater:
\[ \text{Difference} = 462 - 350 = 112 \, \text{cm}^3 \]

### Final Answer:
The circular can has a greater capacity than the plastic can by **112 cm³**.