Question

Total surface area of a cube is 32 2/3 meter cube . Find the volume of the cube

Answer 1

Step-by-step explanation:

$Total \: surface \: area \: of \: cube \\ = 32 \frac{2}{3} = \frac{32 \times 3 + 2}{3} = \frac{98}{3} {m}^{2} \\ \because \: Total \: surface \: area \: of \: cube \\ = 6{a}^{2} (a \: = side \: of \: cube) \\ \therefore \: 6{a}^{2} = \frac{98}{3} \\ \therefore {a}^{2} = \frac{98}{3 \times 6} \\ \therefore {a}^{2} = \frac{49}{3 \times 3} \\ \therefore {a}^{2} = \frac{49}{9} \\ \therefore {a} = \frac{7}{3} \: m \\ volume \: of \: cube \: = {a}^{3} \\ = ( \frac{7}{3})^{3} \\ = \frac{343}{27} \: {m}^{3} \\thus \\ \boxed{ volume \: of \: cube \: = \frac{343}{27} \: {m}^{3}}$

Answer 2

The volume of the cube is $=12\dfrac{19}{27}\ m^3$  .

Explanation:

Let a be the sides of cube.

Total surface area of cube = 6a²

Volume of cube = a³

Given : Total surface area of a cube = $32\dfrac{2}{3}\ m^3=\dfrac{98}{3}\ m^3$

$\Rightarrow\ 6a^2=\dfrac{98}{3}\\\\\Rightarrow\ a^2=\dfrac{98}{3\times6}=\dfrac{49}{9}=(\dfrac{7}{3})^2\\\\\Rightarrow\ a=\dfrac{7}{3}\ m$

Now volume of cube = $(\dfrac{7}{3})^3=\dfrac{7^3}{3^3}=\dfrac{343}{27}\ m^3$

$=12\dfrac{19}{27}\ m^3$

Hence, the volume of the cube is $=12\dfrac{19}{27}\ m^3$

# Learn more :

The volume of a cube is double the volume of a cuboid. If the volume of the cuboid is 6.912cm cube. Find the length of an edge of cube..

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