Conical Heap and Food Grain Donation

To solve this problem, we need to find the amount of tarpulin needed to cover the remaining grain after the farmer donates half of it to an orphanage. We also need to determine the amount of grain the farmer donated and discuss the values we can learn from this act of kindness.

Given Information:
- Slant height of the heap (l) = 35 cm
- Circumference of the base (C) = 132 cm

Calculating the Radius:
The circumference of a circle is given by the formula C = 2πr, where r is the radius. We can rearrange this formula to solve for the radius:
r = C / (2π) = 132 cm / (2π) ≈ 21 cm

Calculating the Volume of the Heap:
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. In this case, the height is the slant height (l). Substituting the known values:
V = (1/3)π(21 cm)²(35 cm) ≈ 38,535 cm³

Calculating the Donated Grain:
Since the farmer donates half of the grain, the remaining grain will be half of the initial amount. Therefore, the amount of grain donated is also half of the initial volume:
Donated Grain = 0.5 * 38,535 cm³ = 19,267.5 cm³

Calculating the Tarpulin Needed:
To cover the remaining grain, we need to find the surface area of the base of the heap. The surface area of a circle is given by the formula A = πr². Substituting the known radius:
Base Area = π(21 cm)² ≈ 1385.44 cm²

Therefore, the amount of tarpulin needed to cover the remaining grain is approximately 1385.44 cm².

Values Learned from this Act:
1. Kindness and empathy: The act of donating food grain to an orphanage demonstrates kindness and empathy towards those in need. It helps to provide sustenance and support to less fortunate children.
2. Sharing and generosity: By donating half of the grain, the farmer exemplifies the value of sharing and generosity, spreading the resources and benefits among others.
3. Community support: This act of donation strengthens the sense of community and encourages others to contribute towards the well-being of society.
4. Responsibility and social consciousness: The farmer takes responsibility for the welfare of the orphanage children and shows social consciousness by recognizing their needs and taking action to fulfill them.
5. Gratitude and appreciation: The orphanage children benefit from the farmer's act of kindness, fostering gratitude and appreciation for the help they receive from others.

This act of donating food grain not only fulfills the immediate needs of the orphanage children but also promotes values that contribute to a more compassionate and caring society.

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