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.
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:
\[ \text{Surface Area} = 2(\text{Length} \times \text{Height} + \text{Length} \times \text{Width} + \text{Height} \times \text{Width}) \]
To find the width of a rectangular prism using volume, you need to:
To find the width of a rectangular prism using surface area, you need to:
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.
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.
