Final answer:
To calculate the total volume of grains a silo can hold, add the volume of its cylindrical and conical parts using the formulas for volume of a cylinder (V = πr²h) and a cone (V = ⅓πr²h), ensuring to use the correct dimensions for each part.
Step-by-step explanation:
In mathematics, specifically in geometry, to calculate the total volume of grains that can be stored in a silo, one must consider the shapes involved in the structure of the silo. If the silo consists of a cylindrical portion and a conical portion, the correct way to find the total volume is to calculate the volume of each part separately and then add them together.
For the cylinder, use the formula V = πr²h, where 'r' is the radius and 'h' is the height of the cylinder. For the cone, the formula is V = ⅓πr²h, where 'r' is the radius of the base of the cone and 'h' is the height of the cone.
Thus, to combine these and find the total volume of such a silo, we would use the sum of the volumes of the cylinder and the cone:
π(8.5ft)²(2ft) + ⅓π(2ft)²(13ft - 8.5ft),
where the first term represents the volume of the cylindrical part and the second term the volume of the conical part, assuming that the radii and heights given are correct for each part of the silo.