Final answer:
To find the volume of a sandpile which is shaped like a cone, we use the slant height and the angle with the ground to calculate the radius and height, and then apply the formula for the volume of a cone.
Step-by-step explanation:
To calculate the volume of the sandpile, we need to determine the shape of the sandpile first. Given the description, it is logical to assume the sandpile has a conical shape. Now, to calculate the volume of a cone, we use the formula:
V = ⅓ π r^2 h
Where V is the volume, r is the radius of the base, h is the height, and π is Pi (approximately 3.14159). Given the slant height (RT) and the angle (40°), we can calculate the radius (r) and the height (h) of the sandpile using trigonometric relations.
Let's calculate the radius (r) and height (h) using the following trigonometric functions:
- Sin(40°) = h / 20m
- Cos(40°) = r / 20m
By solving these equations, we find:
- h = 20m * Sin(40°)
- r = 20m * Cos(40°)
Once we have the values for r and h, we substitute them back into the volume formula to find the volume of the sandpile.
The calculations are as follows:
- h = 20m * 0.6428 (approximate value of Sin(40°))
- r = 20m * 0.7660 (approximate value of Cos(40°))
- V = ⅓ π (20m * 0.7660)^2 * (20m * 0.6428)
After performing the calculation, we round the volume to the nearest cubic meter to get the final answer.