Question : If the surface area of a cube is 5046 cm2, then the volume of the cube is:
Option 1: 26189 cm3
Option 2: 25145 cm3
Option 3: 22812 cm3
Option 4: 24389 cm3
Correct Answer: 24389 cm 3
Solution :
Given: The surface area of a cube is 5046 cm
2
.
The surface area of a cube is given by $6a^2$, where $a$ is the length of a side.
$a = \sqrt{\frac{5046}{6}} = 29$ cm
The volume $(V)$ of a cube is given by $a^3$.
$V = a^3 = (29)^3 = 24389$ cm
3
Hence, the correct answer is 24389 cm
3
.
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