A cylindrical cardboard mailing tube has a diameter of 5 in. and a height of 30 in. A total of 30% of the tube's capacity is filled with spherical packing foam. Each foam sphere has a diameter of 0.6 in. Approximately how many pieces of foam are in a tube?

Question

Poncho

Mathematics

18 July, 02:41

A cylindrical cardboard mailing tube has a diameter of 5 in. and a height of 30 in. A total of 30% of the tube's capacity is filled with spherical packing foam. Each foam sphere has a diameter of 0.6 in. Approximately how many pieces of foam are in a tube?

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Answers (1)

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Kaiser · Answer 1

First is to get the volume of the cylinder.

Volume = pi * r^2 * H

Volume = 3.1416 * (5/2) ^2 * 30

Volume = 589.05 in^3

30% is already filled.

Filled Space = 589.05 * 0.30

Filled Space = 176.715 in^3

Empty Space = 412.335 in^3

Next, get the volume of the sphere.

V = (4/3) * pi*r^3

V = (4/3) * pi * (0.6/2) ^3

V = 0.1130976 in^3

Number of foams = Filled Space / V

Number of foams = 176.715 / 0.1130976

Number of foams = 1562 Foams