Two types of water tankers are available in a shop. One is in cubic form of dimensions 1m x 1m x 1m and another is in cylindrical form of diameter 1 m and height Im.
(i) Calculate the volume of both the tankers.
(ii) The shopkeeper advices you to purchase a cuboid tank. Which value is depicted by the shopkeeper?

Answer

### Step-by-Step Solution:

**(i) Calculate the volume of both the tankers.**

1. **Volume of the Cubic Tank:**
- The dimensions of the cubic tank are given as 1m x 1m x 1m.
- The formula for the volume \( V \) of a cube is:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
- Substituting the values:
\[ V = 1 \, \text{m} \times 1 \, \text{m} \times 1 \, \text{m} = 1 \, \text{m}^3 \]

2. **Volume of the Cylindrical Tank:**
- The diameter of the cylindrical tank is given as 1m, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{1 \, \text{m}}{2} = 0.5 \, \text{m} \]
- The height \( h \) of the cylindrical tank is also 1m.
- The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
- Substituting the values:
\[ V = \pi (0.5 \, \text{m})^2 (1 \, \text{m}) = \pi \times 0.25 \, \text{m}^2 \times 1 \, \text{m} = \frac{\pi}{4} \, \text{m}^3 \]
- Approximating \( \pi \) as 3.14:
\[ V \approx \frac{3.14}{4} \approx 0.785 \, \text{m}^3 \]

3. **Comparison of Volumes:**
- The volume of the cubic tank is \( 1 \, \text{m}^3 \).
- The volume of the cylindrical tank is approximately \( 0.785 \, \text{m}^3 \).
- Therefore, the volume of the cubic tank is greater than that of the cylindrical tank.

**(ii) The shopkeeper advises you to purchase a cuboidal tank. Which value is depicted by the shopkeeper?**
- The shopkeeper is likely considering the benefit of the customer. By recommending the cubic tank, which has a larger volume, the shopkeeper is demonstrating customer-friendly behavior, ensuring that the customer gets more storage capacity for their needs.