Question

Task 2: A storage container, in the shape of a cone with a diameter of 40ft and height of 30ft, is used to store grain. The farmer would like to replace the cone with a cylindrical shaped container such that it covers the same area on the ground but stores 6 times as much grain as the cone. How tall does the cylinder need to be and how much grain will it hold after construction?

          Task 2: A storage container, in the shape of a cone with a diameter of 40ft and
height of 30ft, is used to store grain. The farmer would like to replace the cone
with a cylindrical shaped container such that it covers the same area on the
ground but stores 6 times as much grain as the cone. How tall does the
cylinder need to be and how much grain will it hold after construction?

Task 2: A storage container, in the shape of a cone with a diameter of 40ft and
height of 30ft, is used to store grain. The farmer would like to replace the cone
with a cylindrical shaped container such that it covers the same area on the
ground but stores 6 times as much grain as the cone. How tall does the
cylinder need to be and how much grain will it hold after construction?

Added by Michele W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Daniel Pyda

Step 1

The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. Given that the diameter of the cone is 40 ft, the radius (r) is half of the diameter, so r = 40/2 = 20 ft. The height of the cone is given as 30 ft. Plugging Show more…

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Task 2: A storage container, in the shape of a cone with a diameter of 40 ft and height of 30 ft, is used to store grain. The farmer would like to replace the cone with a cylindrical shaped container such that it covers the same area on the ground but stores 6 times as much grain as the cone. How tall does the cylinder need to be and how much grain will it hold after construction?