A soft drink can has a circular base diameter 7 cm and height 12 cm. A powder tin has a square base with side 7 cm and height 12 cm. What is the difference in their capacities ?

Answer

To find the difference in capacities between a soft drink can (cylindrical) and a powder tin (cuboidal), we will first calculate the volume of each container and then find the difference.

### Step 1: Calculate the volume of the soft drink can (cylinder)

The formula for the volume \( V \) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius of the base
- \( h \) is the height of the cylinder

**Given:**
- Diameter of the can = 7 cm
- Height of the can = 12 cm

**Calculate the radius:**
\[ r = \frac{\text{Diameter}}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

**Now, substitute the values into the volume formula:**
\[ V = \pi (3.5)^2 (12) \]

Calculating \( (3.5)^2 \):
\[ (3.5)^2 = 12.25 \]

Now substituting back:
\[ V = \pi \times 12.25 \times 12 \]
\[ V = \pi \times 147 \]

Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 147 \]
\[ V = 22 \times 21 = 462 \text{ cm}^3 \]

### Step 2: Calculate the volume of the powder tin (cuboid)

The formula for the volume \( V \) of a cuboid is given by:

\[ V = \text{length} \times \text{width} \times \text{height} \]

**Given:**
- Side of the square base = 7 cm
- Height = 12 cm

**Substituting the values:**
\[ V = 7 \times 7 \times 12 \]
\[ V = 49 \times 12 = 588 \text{ cm}^3 \]

### Step 3: Calculate the difference in capacities

Now, we will find the difference between the volumes of the powder tin and the soft drink can:

\[ \text{Difference} = \text{Volume of powder tin} - \text{Volume of soft drink can} \]
\[ \text{Difference} = 588 \text{ cm}^3 - 462 \text{ cm}^3 \]
\[ \text{Difference} = 126 \text{ cm}^3 \]

### Final Answer:
The difference in their capacities is **126 cm³**.

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