Question

a student interpreted a volume of 8 cm³ on the cube shown. what is wrong with this interpretation?
choose the correct answer below.
o a. the given box has a volume of 64 cm³ and not 8 cm³. the student most likely thinks 8 cm³ means (8 cm)².
o b. the given box has a volume of 512 cm³ and not 8 cm³. the student most likely thinks 8 cm³ means (8 cm)³.
o c. the given box has a volume of 24 cm³ and not 8 cm³. the student most likely thinks 8 cm³ means 8 cm + 8 cm + 8 cm.
o d. the student is correct.

Explanation:

Step1: Recall the volume formula for a cube

The volume formula for a cube is \(V = s^3\), where \(s\) is the side - length of the cube.

Step2: Calculate the volume of the given cube

Given \(s = 8\mathrm{cm}\), then \(V=(8\mathrm{cm})^3=8\times8\times8 = 512\mathrm{cm}^3\).

Step3: Analyze each option

• Option A: \((8\mathrm{cm})^2=64\mathrm{cm}^2\) (this is the formula for the area of a square, not the volume of a cube).
• Option B: \((8\mathrm{cm})^3 = 512\mathrm{cm}^3\) (correct volume formula for the cube).
• Option C: \(8 + 8+8=24\) (this is the formula for the sum of the side - lengths, not the volume).
• Option D: The student is not correct.

Answer:

B. The given box has a volume of \(512\mathrm{cm}^3\) and not \(8\mathrm{cm}^3\). The student most likely thinks \(8\mathrm{cm}^3\) means \((8\mathrm{cm})^3\).