Final answer:
To find the volume of a right circular cone, calculate the radius from the given circumference and then use the formula V = (1/3)πr²h, substituting the values for radius (r) and height (h), and finally rounding the result to the nearest tenth.
Step-by-step explanation:
The student has asked for the volume of a right circular cone with a known height and the circumference of its base. To find the volume, we need the radius of the base, which we can calculate using the formula for the circumference of a circle, C = 2πr.
Once we have the radius, we can use the formula for the volume of a cone, which is V = (1/3)πr²h.
First, we calculate the radius from the given circumference:
- C = 16.3 in
- 16.3 = 2πr
- r = 16.3 / (2π)
Upon finding the radius, we then plug it into the volume formula:
V = (1/3)πr²(17.1)
With calculations, the student will end up with an answer in cubic inches, which they will then round to the nearest tenth as instructed.