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How to Find Surface Area With the Volume of a 3D Object

Calculating the surface area and volume of a three-dimensional object is important in many fields such as logistics, which is the planning and arranging for the transport or shipping of items. To properly plan for a move or for storing a number of items, you must have a detailed accounting of the number of containers, their sizes and their volume. The calculation of these figures depends on the shapes of the boxes and their dimensions. Each shaped 3-D container uses a different formula for the calculation of the surface area and for the volume. You can examine this set of calculations by using a rectangular box as the object.

Things You'll Need

  • Rectangular box
  • Tape measure
  • Calculator
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Instructions

    • 1

      Measure the rectangular box with a tape measure and record the dimensions. There are three dimensions to obtain for a rectangular box: the height, the width and the length. For example purposes, assume you obtained the measurements of height = 24 inches, width = 30 inches and length = 48 inches.

    • 2

      Write down the formula for the calculation of the volume and surface area of the object. For a rectangular box the volume is obtained by the equation: volume = length * width * height. Its length multiplied by its width obtains surface area of each face of the box. You must remember there are six faces of the box that you need to be calculate. The front and back faces are the same, the right side and left side are the same and the top and bottom faces are the same. Therefore, the equation for the surface area of the rectangular box is surface area = 2 * (length * width) + 2 * (height * width) + 2 * (length * height).

    • 3

      Insert the measurements taken of the rectangular box and evaluate the surface area and volume of the box. To obtain the answers in square feet and cubic feet, convert the dimensions from inches to feet. Continuing the example, to obtain the answers for surface area and volume of the box in square feet and cubic feet, convert the dimensions from inches to feet. Multiply each of the measurements by 1 foot / 12 inches. Height = 24 inches * 1/12 = 2 feet, width = 30 inches * 1/12 = 2.5 feet, and length = 48 inches * 1/12 = 4 feet. Calculate the volume = length * width * height = 2 feet * 2.5 feet * 4 feet = 20 cubic feet. The surface are of the box is surface area = 2 * (length * width) + 2 * (height * width) + 2* (length * height) = (2 * 4 * 2.5) + (2 * 2 * 2.5) + (2 * 2 * 4) = 20 + 10 + 16 = 46 square feet.

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