Final answer:
To find the height of the tree stump, calculate the radius using the formula for circumference, then use the volume formula to solve for height. The height of the tree stump is approximately 3.1 feet.
Step-by-step explanation:
To find the height of the tree stump, we need to calculate the radius of the stump and then use that along with the volume of the stump to find the height.
Given that the circumference of the stump is 84 inches, we can use the formula for circumference of a cylinder, which is 2πr, where r is the radius.
Therefore, 2πr = 84 inches. Solving for r, we have r = 84 inches / (2π) = 13.369 inches.
Next, we can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume and h is the height.
Substituting the given volume of the stump as 20214 cubic inches and the calculated radius as 13.369 inches, we can solve for h:
20214 cubic inches = π(13.369 inches)²h
Dividing both sides of the equation by π(13.369 inches)² gives h = 20214 cubic inches / (π(13.369 inches)²) = 37.785 inches.
Finally, we convert the height from inches to feet by dividing by 12: 37.785 inches / 12 = 3.149 feet.
Therefore, the height of the tree stump is approximately 3.1 feet.