Sure, let's solve the problem step-by-step:
1. Calculate the Radius of Each Well:
- The radius is half of the diameter.
- For Salman’s well:
[tex]\[
\text{Radius of Salman’s well} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \text{ meters}
\][/tex]
- For Pramila’s well:
[tex]\[
\text{Radius of Pramila’s well} = \frac{\text{Diameter}}{2} = \frac{18}{2} = 9 \text{ meters}
\][/tex]
2. Calculate the Area Occupied by Each Well:
- The area of a circle is given by the formula [tex]\(A = \pi r^2\)[/tex].
- For Salman’s well:
[tex]\[
\text{Area of Salman’s well} = \pi \times (\text{Radius})^2 = 3.14 \times (7)^2
\][/tex]
[tex]\[
\text{Area of Salman’s well} = 3.14 \times 49 = 153.86 \text{ square meters}
\][/tex]
- For Pramila’s well:
[tex]\[
\text{Area of Pramila’s well} = \pi \times (\text{Radius})^2 = 3.14 \times (9)^2
\][/tex]
[tex]\[
\text{Area of Pramila’s well} = 3.14 \times 81 = 254.34 \text{ square meters}
\][/tex]
3. Determine Whose Well Occupies More Land and By How Much:
- Compare the areas calculated:
[tex]\[
\text{Area of Pramila’s well} = 254.34 \text{ square meters}
\][/tex]
[tex]\[
\text{Area of Salman’s well} = 153.86 \text{ square meters}
\][/tex]
- Pramila’s well occupies more land.
- Calculate the difference in the area occupied:
[tex]\[
\text{Difference in areas} = \text{Area of Pramila’s well} - \text{Area of Salman’s well}
\][/tex]
[tex]\[
\text{Difference in areas} = 254.34 - 153.86 = 100.48 \text{ square meters}
\][/tex]
So, Pramila’s well occupies more land than Salman’s well, and the difference in the area occupied by their wells is 100.48 square meters.
