Ellie's bird feeder is shaped like a cone with a height of 24 in. and a radius of 3 in. Packages of bird seed are cylindrical and come in different sizes. Solve for the height of the package that has a radius of 6 in. and contains exactly enough bird seed to fill the feeder. Use 3.14 to approximate pi.

Question

Matthias

Mathematics

29 July, 22:53

Ellie's bird feeder is shaped like a cone with a height of 24 in. and a radius of 3 in. Packages of bird seed are cylindrical and come in different sizes. Solve for the height of the package that has a radius of 6 in. and contains exactly enough bird seed to fill the feeder. Use 3.14 to approximate pi.

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Skyler Cohen · Answer 1

The volume of seeds in the package must be equal to the volume of the feeder in order to fill it completely. The volume of the conic feeder is given by:

V (f) = (πr²h) / 3

And volume of the cylindrical package is given by:

V (p) = πr²h

Equating the two and substituting values:

(π x 3² x 24) / 3 = π x 6² x h

h = 2 inches