Weigh the Iron Plate with Holes

Here’s a fun math problem for you iron workers (current and future) out there!

The formula for calculating the weight of iron is:

  • 1” x 12” x 12” = 40 Lbs

The dimensions of this plate shown in the picture below are:

  • 3’9” x 3’2” x 8”

The plate also has 13 holes with a diameter of 2.5”.

What is the weight of this plate?

See below for hints…


Find the volume of the 40 pound plate of Iron

  1. Calculate the weight per cubic inch of Iron
  2. Calculate the volume of the Iron plate in the picture without holes.
  3. Calculate the volume of the holes.
  4. Find the total volume of the plate in the picture with the holes.
  5. Find the weight of the plate in the picture.

See below for the answer…


Volume of a plate = Height * Width * Depth

Volume of a Cylinder = π * radius * height

  1. volume of the 40 pound plate of Iron: 144 in^3
  2. weight per cubic inch of Iron: 40 / 144 = 0.278 lbs
  3. volume of the Iron plate in the picture without holes: 8 * 45 * 38 = 13680 in^3
  4. Calculate the volume of the holes: 13 * 39.2699 = 510.5087 in^3
  5. volume of the plate in the picture with the holes: 13169.4913 in^3
  6. Weight of the plate in the picture: 3658.192028 pounds

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