Finding a Missing Dimension of a Rectangular Prism
Finding a Missing Dimension of a Rectangular Prism is a Grade 5 math skill from Illustrative Mathematics Chapter 4 (Wrapping Up Multiplication and Division with Multi-Digit Numbers) where students use the volume formula V = l × w × h to solve for an unknown dimension by dividing the volume by the product of the two known dimensions. This applies the inverse relationship between multiplication and division.
Key Concepts
If you know the volume of a rectangular prism and two of its three dimensions (length, width, height), you can find the missing dimension by using division.
Given the volume formula $V = l \times w \times h$: $$h = \frac{V}{l \times w} \quad \text{or} \quad l = \frac{V}{w \times h} \quad \text{or} \quad w = \frac{V}{l \times h}$$.
Common Questions
How do you find a missing dimension of a rectangular prism given its volume?
Divide the volume by the product of the two known dimensions. For example, if V = 504, l = 9, w = 7, then h = 504 ÷ (9 × 7) = 504 ÷ 63 = 8 cm.
What formula is used to find a missing dimension of a prism?
Rearrange V = l × w × h. To find height: h = V ÷ (l × w). To find length: l = V ÷ (w × h). To find width: w = V ÷ (l × h).
What chapter covers missing prism dimensions in Illustrative Mathematics Grade 5?
Finding a missing dimension of a rectangular prism is covered in Chapter 4 of Illustrative Mathematics Grade 5, titled Wrapping Up Multiplication and Division with Multi-Digit Numbers.
Why does dividing volume by two dimensions give the third dimension?
The volume formula V = l × w × h can be rearranged. Dividing both sides by (l × w) gives h = V ÷ (l × w). Division is the inverse of multiplication, so it undoes the multiplication of the known dimensions.
What is an example of finding a missing prism dimension?
A box has V = 1,320 ft³, w = 10 ft, h = 11 ft. Find length: l = 1,320 ÷ (10 × 11) = 1,320 ÷ 110 = 12 ft.