If the perimeter of one face of a cube is $ 48 ext{ cm}$, then its volume is:

Question

If the perimeter of one face of a cube is $ 48 	ext{ cm}$, then its volume is:

Examoogle · Accepted Answer

The correct answer is Option B: $1728 	ext{ cm}^3$. Since the perimeter of a square face is $4a$, divide $48$ by $4$ to get side $a = 12$ cm, then cube it ($12^3 = 1728$).

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the perimeter of a square face is $4a$, divide $48$ by $4$ to get side $a = 12$ cm, then cube it ($12^3 = 1728$).

Formula Used: $$V = a^3$$

Given: Perimeter of one face of a cube = 48 cm

Steps: Understand the given information: A cube has 6 identical square faces. The perimeter of one face is given as $48	ext{ cm}$.. Find the side length of the cube: Since each face is a square with side $a$, its perimeter is $4a$. Dividing $48$ by $4$ gives the side length $a$.. Calculate the volume of the cube: The formula for the volume of a cube is $V = a^3$. Substituting $a = 12	ext{ cm}$ into the formula:

Answer: B is correct because the side length of the cube is $12	ext{ cm}$ and its volume is $12^3 = 1728	ext{ cm}^3$.

Exam Tip: Always verify whether the question refers to the perimeter of a single face ($4a$), total edge length ($12a$), or total surface area ($6a^2$) before calculating volume.

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