SOLUTION: Please help me solve this word problem: A well 40 ft. deep and 6.5 ft. in diameter is lined with stone 1.5 ft. thick so that the inner diameter of the well becomes 3.5 ft. Find the
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Question 1188054: Please help me solve this word problem: A well 40 ft. deep and 6.5 ft. in diameter is lined with stone 1.5 ft. thick so that the inner diameter of the well becomes 3.5 ft. Find the number of cubic feet of stone required. Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the well is 40 feet deep.
the diameter of the well is 6.5 feet in diameter.
it is lined with 1.5 feet thick wall of stone so that the inner diameter of the well becomes 3.5 feet.
the volume of the cylinder is equal to pi * r^2 * h.
the outer volume of the well, including the stone walls, is equal to pi * (6.5/2)^2 * 40 * pi = 422.5 * pi cubic feet.
the inner volume of the well is equal to (3.5)^2 * 40 * pi = 122.5 * pi cubic feet.
the difference between the inner volume and the outer volume is equal to 422.5 * pi minus 122.5 * pi = 300 cubic feet.
that's the number of cubic feet of stone in the well.
pi is equal to a constant value of 3.141592654.
422.5 * pi cubic feet = 1327.322896 cubic feet.
122.5 * pi cubic feet = 384.8451001 cubic feet.
the number of cubic feet of stone is equal to 300 * pi cubic feet = 942.4777961 cubic feet.
In his solution on the way, tutor @Theo made several errors.
So, I came to bring a correct solution.
The volume of the well before filling with the stone
V = = = 1326.65 cubic feet.
The inner volume of the well AFTER filling with the stone
v = = = 384.65 cubic feet.
The volume of the stone is the difference of volumes
= V - v = 1326.65 - 384.65 = 942 cubic feet. ANSWER
