Final answer:
To find the volume of a redwood tree trunk, which is cylindrical, use the formula for a cylinder's volume V = πr^2h. The circumference of 20π ft gives a radius of 10 ft, and with a height of 100 ft, the approximate volume is V ≈ 31,416 ft^3.
Step-by-step explanation:
The volume of the redwood tree trunk can be determined by treating it as a cylinder. To find the volume of a cylinder, the formula V = πr^2h is used, where 'r' is the radius of the base and 'h' is the height of the cylinder. Given the circumference of the trunk is 20π ft, we can deduce the diameter of the trunk to be 20 ft, and therefore, the radius is 10 ft (since radius is half the diameter). The height of the tree is provided as 100 ft. Now we can calculate the volume.
V = π(10 ft)^2(100 ft)
Thus, simplifying:
V = π(100 ft)(100 ft) = 10,000π ft^3
To find an approximate value, we multiply 10,000 by 3.1416 (an approximation for π):
V ≈ 31,416 ft^3