The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
Question
The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
Solution
The volume V of a right cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.
In this case, we know the volume V is 13685 cubic inches and the radius r is 11 inches. We want to find the height h.
We can rearrange the formula to solve for h: h = V / (πr²).
Substituting the given values into the formula gives us: h = 13685 / (π * 11²).
Calculating this gives us the height of the tree stump.
Let's calculate it:
h = 13685 / (π * 121) = 35.7 inches.
So, the height of the tree stump is approximately 35.7 inches.
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