Rectangular Prism Width Calculator

Calculate Width Using Volume or Surface Area









Definition

A rectangular prism consists of three different dimensions: length, height, and width. These dimensions create its volume and surface area, which are its internal and external measurements, respectively. When you know two of the dimensions and either the volume or surface area, you can find the third dimension.

Formulas

To find the width of a rectangular prism using volume:

\[ \text{Volume} = \text{Length} \times \text{Height} \times \text{Width} \]

To find the width of a rectangular prism using surface area:

\[ \text{Surface Area} = 2(\text{Length} \times \text{Height} + \text{Length} \times \text{Width} + \text{Height} \times \text{Width}) \]

Description

To find the width of a rectangular prism using volume, you need to:

  1. Obtain the length, height, and volume of the rectangular prism.
  2. Multiply the length by the height.
  3. Divide the volume by the product of the length and height to calculate the width.

To find the width of a rectangular prism using surface area, you need to:

  1. Obtain the length, height, and surface area of the rectangular prism.
  2. Multiply the length by the height, and then double the product.
  3. Subtract the doubled product from the surface area.
  4. Double the length and height, then add the two products together.
  5. Divide the difference from Step 3 by the sum from Step 4 to calculate the width.

Example Calculation Using Volume

For a rectangular prism with a length of 20 inches, height of 20 inches, and volume of 4,000 cubic inches:

\[ 20 \times 20 = 400 \, \text{square inches} \] \[ 4000 \div 400 = 10 \, \text{inches} \]

The width is 10 inches.

Example Calculation Using Surface Area

For a rectangular prism with a length of 10 inches, height of 10 inches, and surface area of 400 square inches:

\[ 10 \times 10 = 100 \, \text{square inches} \] \[ 100 \times 2 = 200 \, \text{square inches} \] \[ 400 - 200 = 200 \, \text{square inches} \] \[ 10 \times 2 = 20 \, \text{inches} \] \[ 20 + 20 = 40 \, \text{inches} \] \[ 200 \div 40 = 5 \, \text{inches} \]

The width is 5 inches.