Columbia Records unveiled the LP (a vinyl record) in the Waldorf Astoria on June 18, 1948, in two formats: inches in diameter, matching that of 78 rpm singles, and inches in diameter. If the thickness of one vinyl record is then determine the difference in volumes between the inch and inch records.

Difference in volume between the two vinyl records = 3.872 in³

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Complete Question

2columbia records unveiled the lp (a vinyl record) in the waldorf astoria on june 18, 1948, in two formats: 10 inches in diameter, matching that of 78 rpm singles, and 12 inches in diameter. if the thickness of one vinyl record is 0.112 in, then determine the difference in volumes between the 10 inch and 12 inch records.

Each of the vinyl records will be modelled as a cylinder

Volume of a cylinder = πr²h

For the 12 inches diameter records.

r = (12/2) = 6 inches

h = thickness = 0.112 inches

Volume = π × (6²) × 0.112 = 12.672 in³

For the 10 inches diameter records

r = (10/2) = 5 inches

h = thickness = 0.112 inches

Volume = π × (5²) × 0.112 = 8.8 in³

Difference in volume between the two vinyl records = 12.672 - 8.8 = 3.872 in³

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