Question : If the volume of a cube is 1728 cm3, then what is the total surface area of the cube?
Option 1: 804 cm2
Option 2: 729 cm2
Option 3: 864 cm2
Option 4: 926 cm2
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Correct Answer: 864 cm 2
Solution :
The volume of a cube is given by the formula $V = a^3$, where $a$ is the length of a side.
Given that the volume $V$ is 1728$\text{ cm}^3$,
$a = \sqrt[3]{V} = \sqrt[3]{1728} = 12 \text{ cm}$
So, the total surface area $A$ of a cube,
$A = 6a^2$
Substituting $a = 12$$\text{ cm}^2$,
$⇒A = 6 \times (12)^2 = 6 \times 144 = 864 \text{ cm}^2$
Hence, the correct answer is 864 cm
2
.
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