Let’s solve this step by step.
We are told:
- The density of air is
1.20 kg/m³.
- We need to find the mass of air in a room that is
5 m long, 4 m wide, and 3 m high.
---
Step 1: Find the volume of the room
Volume = length × width × height
→ Volume = 5 m × 4 m × 3 m
→ Volume =
60 m³
---
Step 2: Use density formula to find mass
Density = mass / volume
So, rearranged:
Mass = Density × Volume
Plug in the numbers:
Mass = 1.20 kg/m³ × 60 m³
→ Mass =
72 kg
---
Wait — let’s check the student’s work in the image (even though we don’t describe it, we can use it to verify).
The student wrote:
> 1.20 kg/m³ × (5×4×3) m³ = ?
> Then they did: 1.20 × 60 = 72 → but then crossed out and wrote “19.9”?? That doesn’t make sense.
Actually, looking at their scribbles, they might have mistakenly used 1.20 × 16.6 or something? But no — 5×4×3 is definitely 60.
Also, note: sometimes people confuse units — but here everything is in meters and kg/m³, so no conversion needed.
Another possible mistake: maybe they thought “density of air is 1.20 g/L”? Let’s check that just in case.
If someone misreads density as 1.20 g/L:
- 1 m³ = 1000 L → so 60 m³ = 60,000 L
- 1.20 g/L × 60,000 L = 72,000 g = 72 kg → same answer!
So even if you convert via grams and liters, you still get 72 kg.
But wait — the student wrote “19.9” somewhere? Maybe they multiplied 1.20 × 16.6? Where would 16.6 come from?
Ah! Perhaps they calculated surface area instead of volume?
Surface area of a rectangular prism = 2(lw + lh + wh)
= 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2(47) = 94 m² — not 16.6.
Or maybe they did 5+4+3 = 12? No.
Alternatively, perhaps they divided instead of multiplied?
1.20 ÷ 60 = 0.02 — nope.
Wait — another idea: maybe they used feet? But the problem says meters.
No — the correct calculation is straightforward.
Let me double-check multiplication:
1.20 × 60
= 1.2 × 6 × 10
= 7.2 × 10
=
72
Yes.
Perhaps the student made an error in writing “19.9” — maybe that was for a different part? Or maybe they meant 72 but wrote wrong?
Looking again — in the red ink, there’s “1.20 kg/m³ × ___ = ___ kg”, and below that “19.9” — but also “2.988” and “0.8 mL” which seem unrelated.
Actually, those other numbers look like they belong to other problems on the page (like liquid volumes or something). So probably the student got confused with multiple questions.
For THIS question — mass of air in room — it’s simply:
Mass = density × volume = 1.20 × 60 = 72 kg
Final Answer:
72
Parent Tip: Review the logic above to help your child master the concept of mole conversion worksheet answer key.
