Final answer:
To address the student's geometry question about a conical wheat heap, the slant height is calculated using the Pythagorean theorem, the canvas cloth area needed is found with the lateral surface area formula, and the volume and base area are calculated using their respective geometric formulas.
Step-by-step explanation:
The calculations in this question revolve around a conical heap of wheat and are based on principles of geometry:
To find the slant height, we use the Pythagorean theorem, considering the radius (half of the diameter) and the height of the cone.
The surface area needed to cover the heap can be calculated with the formula for the lateral surface area of a cone, which requires the slant height and the radius.
The volume of the cone can be found using the formula for the volume of a cone.
The base area of the heap is equivalent to the area of a circle with the given diameter.
Steps for Each Calculation:
Slant height (l) of the cone = √(r² + h²), where r is the radius and h is the height.
Surface area (A) for the canvas cloth = πrl, where π is Pi (approx. 3.14159).
Volume (V) of the heap = (1/3)πr²h.
Base area of the field used for making heap = πr².