SOLUTION: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Cu
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-> SOLUTION: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Cu
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Question 1037870: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Currently, the oats that Chris wants to put into the bin is in a cone-shaped pile on the ground. The pile has a diameter of 40 ft and a height of 10.5 ft.
a.Find the volume of oats Chris has in the pile to the nearest cubic foot.
b. Convert the volume of the oats in cubic feet to bush and now find the capacity of the grain bin to the nearest cubic foot.
You can put this solution on YOUR website! the formula for the volume of a cylinder is pi * r^2 * h.
the formula for the volume of a cone is 1/3 * pi * r^2 * h.
r is the radius.
h is the height.
the length of the radius is 1/2 the length of the diameter.
this means the radius of the cylindrical bin is 9.5 feet.
this means the radius of the pile of oats is 20 feet.
the pile of oats on the ground is 40 feet in diameter and 10.5 feet high.
r = 20 feet
h = 10.5 feet
the volume of the oats is equal to 1/3 * pi * r^2 * h which is equal to 1/3 * pi * 20^2 * 10.5 which is equal to 1044 * pi cubic feet.
the volume of the pile of oats is 1044 * pi cubic feet.
the bin has a cylindrical part and a cone part.
the dimensions of the cone part are:
r = 9.5 feet
h = 6 feet
the volume of the cone part is equal to 1/3 * pi * r^2 * h which is equal to 1/3 * pi * 9.5^2 * 6 which is equal to 180.5 cubic feet.
the dimensions of the cylinder part are:
r = 9.5 feet
h = 15 feet
the volume of the cylindrical part is equal to pi * r^2 * h which is equal to pi * 9.5^2 * 15 which is equal to 1353.75 cubic feet.
the total capacity of the cylindrical tank with the cone top is equal to 1353.75 + 180.5 which is equal to 1534.25 cubic feet.
your solutions appear to be:
the volume of the oats is equal to 1044 cubic feet.
the capacity of the tank is equal to 1353.75 cubic feet.
