For the following problems, consider a pool shaped like the bottom half of a sphere, that is being filled at a rate of 25 ft³/min. The radius of the pool is 10 ft. 32. Find the rate at which the depth of the water is changing when the water has a depth of 5 ft.
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The volume V of a sphere is given by the formula V = 4/3πr³. Since the pool is only half a sphere, the volume of the pool is V = 2/3πr³. However, the water in the pool forms a smaller sphere with radius r' that changes as the pool is filled. So, the volume of Show more…
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For the following problems, consider a pool shaped like the bottom half of a sphere, that is being filled at a rate of 25 $\mathrm{ft}^{3} / \mathrm{min}$ . The radius of the pool is 10 $\mathrm{ft}$ . Find the rate at which the depth of the water is changing when the water has a depth of 1 ft.
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For the following problems, consider a pool shaped like the bottom half of a sphere, that is being filled at a rate of 25 ft³/min. The radius of the pool is 10 ft. 32. Find the rate at which the depth of the water is changing when the water has a depth of 5 ft. 33. Find the rate at which the depth of the water is changing when the water has a depth of 1 ft.
Brent B.
For the following problems, consider a pool shaped like the bottom half of a sphere, that is being filled at a rate of 25 $\mathrm{ft}^{3} / \mathrm{min}$ . The radius of the pool is 10 $\mathrm{ft}$ . Using a similar setup from the preceding problem, find the rate at which the gravel is being unloaded if the pile is 5 ft high and the height is increasing at a rate of 4 in./min.
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