Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Find the volume of a cube whose surface area is $384m^2$.
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Answer
Surface area of a cube is given by:
$\text{SA}=6\text{s}^2,$ where $s =$ Side of the cube
Further, volume of a cube is given by:
$\text{V}=\text{s}^3,$ where $s =$ Side of the cube
It is given that the surface area of the cube is $384m^2$. Therefore, we have:
$6\text{s}^2=384$
$\Rightarrow\text{s}=\sqrt{\frac{384}{6}}$
$=\sqrt{64}=8\text{m}$
Now, volume is given by:
$\text{V}=\text{s}^3=8^3$
$\Rightarrow \text{V}=8\times8\times8=512\text{m}^3$
Thus, the required volume is $512m^3$.
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