How To Find The Width Of A Rectangular Prism

A rectangular prism consists of three different dimensions. The prism's length, height and width 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. Find the width of a rectangular prism using the formulas for volume and surface area, which are

\(\text{volume} = \text{ length} × \text{ height} × \text{ width}\)
\(\text{surface area} = (2 × \text{ length}) + (2 × \text{ height}) + (2 × \text{ width})\)

1. Find Values

Obtain the length, height and volume of a rectangular prism. For example, say the length is 20 inches, the height is 20 inches and the volume is 4,000 cubic inches.

2. Multiply Length by Height

Multiply the length by the height. In this example, work out

\(20 × 20 = 400 \text{ square inches}\)

3. Calculate Width

Divide the volume by the product of the length and height to calculate the rectangular prism's width. Work out

\(4,000 ÷ 400 = 10\)

The rectangular prism's width is 10 inches.

1. Find Values

Obtain the length, height and surface area of a rectangular prism. For example, say the length is 10 inches, the height is 10 inches and the surface area is 400 square inches.

2. Multiply Length by Height

Multiply the length by the height, and then double the product. Work out

\(10 × 10 = 100 \text{ square inches}\)

Then work out

\(100 × 2 = 200\)

The answer is 200 square inches.

3. Subtract from Surface Area

Subtract the doubled product of the height and length from the surface area. In this example, work out

\(400 – 200 = 200\)

The answer is 200 square inches.

4. Double Values

Double the length, double the height, then add the two products together. In this example, work out

\(10 × 2 = 20\)

Both the length and the height doubles are 20 inches. Work out

\(20 + 20 = 40\)

The answer is 40 inches.

5. Complete Division

Divide the difference from Step 3 by the sum from Step 4. Work out

\(200 ÷ 40 = 5\)

The width of the rectangular prism is 5 inches.