Rectangular Solids Sample Problems

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Here are some tips for Rectangular Solids, which aligns with New York state standards:

Rectangular Solids

A rectangular solid is a 6-sided prism where all 6 faces are rectangles.

Volume (V) is the amount of space a three-dimensional (3-D) figure occupies. Volume is expressed in cubed units such as mm³, yd³, or ft³. The volume formula for rectangular solids is Volume = Length × Width × Height.

Surface area (S) is the sum of the areas of all the faces, or surfaces, of a three-dimensional (3-D) figure. Surface area is expressed in squared units such as m², cm², or mi². The surface area formula for rectangular solids is Surface area = Sum of the area of all 6 sides.

Example 1:

Find the surface area and volume. Answer with proper units. To represent m², use "sq m". Sample area: 5 sq m. To represent m³, use "cu m"

Surface Area =
Volume =

The answer is Surface Area = Volume =

When using these formulas, it does not matter which edges you assign as length, width, or height as long as you stay with the same assignment.
In the example above, you can use:

• length = 4 ft, width = 2 ft, height = 7 ft, or
• length = 2 ft, width = 7 ft, height = 4 ft, or
• length = 7 ft, width = 4 ft, height = 2 ft