Calculate
(i) area of a square whose side is 1.2 m
(ii) volume of a sphere whose radius is 1.6 cm
(iii) length of a rectangle having area 10.25 `m^2` and breadth 2.5 m

Explanation

Let's solve the question step by step.

### (i) Area of a Square
To calculate the area of a square, we use the formula:
\[ \text{Area} = \text{side}^2 \]
Given that the side of the square is 1.2 m, we can substitute this value into the formula:
\[ \text{Area} = (1.2 \, \text{m})^2 = 1.2 \times 1.2 = 1.44 \, \text{m}^2 \]
Thus, the area of the square is **1.44 m²**.

### (ii) Volume of a Sphere
The formula for the volume of a sphere is:
\[ \text{Volume} = \frac{4}{3} \pi r^3 \]
Here, the radius \( r \) is given as 1.6 cm. We can calculate the volume by substituting the radius into the formula:
\[ \text{Volume} = \frac{4}{3} \pi (1.6 \, \text{cm})^3 \]
Calculating \( (1.6)^3 \):
\[ (1.6)^3 = 1.6 \times 1.6 \times 1.6 = 4.096 \, \text{cm}^3 \]
Now substituting this back into the volume formula:
\[ \text{Volume} = \frac{4}{3} \pi (4.096) \approx \frac{4}{3} \times 3.14 \times 4.096 \approx 17.157 \, \text{cm}^3 \]
Thus, the volume of the sphere is approximately **17.157 cm³**.

### (iii) Length of a Rectangle
To find the length of a rectangle when the area and breadth are given, we use the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
We need to rearrange this formula to solve for length:
\[ \text{Length} = \frac{\text{Area}}{\text{Breadth}} \]
Given that the area is 10.25 m² and the breadth is 2.5 m, we can substitute these values:
\[ \text{Length} = \frac{10.25 \, \text{m}^2}{2.5 \, \text{m}} = 4.1 \, \text{m} \]
Thus, the length of the rectangle is **4.1 m**.

### Summary of Results:
1. Area of the square: **1.44 m²**
2. Volume of the sphere: **17.157 cm³**
3. Length of the rectangle: **4.1 m**