What is the volume of a cube that measures 4.00 cm on each side?
A) 16.0 mL
B) 64.0 L
C) 64.0 mL
D) 64.00 mL
E) 0.640 L
The correct answer and explanation is :
To find the volume of a cube, we use the formula:
[
\text{Volume} = \text{side}^3
]
Given:
- Side length = 4.00 cm
[
\text{Volume} = (4.00\ \text{cm})^3 = 4.00 \times 4.00 \times 4.00 = 64.00\ \text{cm}^3
]
Step 1: Convert cm³ to mL
By definition:
- 1 cubic centimeter (cm³) = 1 milliliter (mL)
So:
[
64.00\ \text{cm}^3 = 64.00\ \text{mL}
]
Step 2: Analyze the choices:
- A) 16.0 mL — Incorrect; this would be the volume of a cube with a smaller side.
- B) 64.0 L — Incorrect; 64.0 L = 64,000 mL.
- C) 64.0 mL — Technically correct in value, but not in significant figures.
- D) 64.00 mL — ✅ Correct: The answer matches both the correct value and the appropriate number of significant figures (3), as given in the side length (4.00 cm has 3 significant figures).
- E) 0.640 L — Incorrect; this equals 640 mL, not 64 mL.
Explanation:
In science, units and significant figures are critical for precision. The side of the cube is given as 4.00 cm, which implies three significant figures. When performing calculations with such measurements, the final answer must reflect the same precision. That’s why the correct answer must be written as 64.00 mL, not 64.0 or 64.
Also, recognizing the conversion between cubic centimeters and milliliters is key. Since 1 cm³ = 1 mL, there’s no need to do a complex conversion—just match the number and convert the unit.