Depth · one concept from first principles · step 2 of 4
Volume needs every length in the same unit
The rectangular prism at the right has a volume of . Find the number that belongs in .
GeometryMeasurement & dataRatios
Your answer
How to solve
Strategy Analyze the Units — Multiplying edges in different units gives nonsense, so make every length a centimeter first -- the volume's unit decides which. Work backwards to the missing edge, then translate that one answer back into meters.
1STEP 1
Put every length in centimeters
The volume is in cubic centimeters, so the edges have to be in centimeters too, and 1 m is 100 cm.
2 × 100 = 200
The known edges are 200 cm and 250 cm.
5.MD.A.1Analyze The UnitsEvery edge has to be measured in the same unit before multiplying.
Why?
A volume in cubic centimetres counts how many one-centimetre cubes fill the box, so each edge has to say how many one-centimetre steps it is.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
A metre is always the same centimetres, so a length given in metres can be renamed in centimetres without changing what it measures.
🧱A bigger unit is a fixed count of smaller unitsA bigger unit always equals the same fixed number of smaller units (1 hour = 60 minutes, 1 km = 1000 m), so a measure can be renamed between them.
2STEP 2
Multiply the two known edges
Their product is the area of the face the missing edge stands on.
200 × 250 = 50000
The base is 50000 cm².
6.G.A.2Identify Subproblems3STEP 3
Work backwards to the missing edge
Volume is base area times the third edge, so divide.
7500000 ÷ 50000 = 150
The third edge is 150 cm.
6.G.A.2Work Backwards4STEP 4
Answer in the unit asked for
The circle is labelled in meters, so convert back.
150 ÷ 100 = 1.5
The circle holds 1.5.
5.MD.A.1Analyze The UnitsAnswer
1.5
Multiply back: 200 × 250 × 150 = 7500000 cm³, the volume given.
Takeaway
Make every length the same unit before multiplying -- the volume's unit tells you which one.
- Put every length in centimeters
- Multiply the two known edges
- Work backwards to the missing edge
- Answer in the unit asked for
Where next?
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