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Question 1031077: A city park contains a cylindrical artificial pond that has a radius of 7.5m. A 2m concrete deck will be constructed around the pond. The concrete should be at least 15cm thick. Calculate the minimum volume of concrete required to construct the deck, to one decimal place. Please Draw a diagram.
Thanks so much :)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the surface area of the pool is equal to area of a circle with a radius of 7.5 meters.
that would be equal to pi * r^2 which is equal to pi * (7.5)^2 which is equal to 176.7145868 square meters.
if you add 2 meters to the radius, then the total surface area of the pool plus the deck surrounding it would be equal to pi * 9.5^2 = 283.528737 square meters.
the surface area of the deck alone would therefore be the surface area of the pool plus the deck minus the surface area of the pool by itself.
that would be 283.528737 square meters minus 176.7145868 square meters which is equal to 106.8141502 square meters.
the thickness of the concrete deck is 15 centimeters.
that's equivalent to 15/100 = .15 meters.
the surface area of the deck constitutes the base of the deck.
the thickness of the deck constitutes the height of the deck.
the volume of a cylindrical solid is equal to the height of the solid * the area of the base.
that means the volume of the deck is equal to .15 * 106.8141502 = 16.02212253 cubic meters.
round that to one decimal place to get 16.0 cubic meters.
to visualize this, consider a smaller cylinder with a radius of 7.5 meters and a height of .15 meters.
the volume would be equal to pi * 7.5^2 * .15 = 26.50718801 cubic meters.
now consider a larger cylinder with a radius of 9.5 meters and a height of .15 meters.
the volume would be equal to pi * 9.5^2 * .15 = 42.52931055 cubic meters.
now remove the volume of the smaller cylinder from the volume of the larger cylinder.
the remaining volume would be equal to 42.52931055 minus 26.50718801 which is equal to 16.02212254 cubic meters.
that's the volume of concrete that you need for the concrete deck surrounding the pool.
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