Question

the volume of a cube is 4096$cm^{3}$. find the total surface area of the cube

Answer 1

Answer:

Below.

Step-by-step explanation:

Each side of the cube = ∛4096

= 16 cm.

Therefore the area of each face  = 16^2 cm^2 and as there are 6 faces:

The total surface area = 6 * 16^2 = 1536 cm^2.

Answer 2

Given :

• Volume = 4096 cm³

To Find :

• Total Surface Area = ?

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SolutioN :

$\dag$ Formula Used :

• Volume(Cube) = Side³
• Total Surface Area (Cube) = 6 × Side²

$\dag$ Calculating the Volume :

$➺ \qquad \;$ Volume = Side³

$\\ ➺ \qquad \;$ 4096 = Side³

$\\ ➺ \qquad \;$ √4096 = Side

$\\ ➺ \qquad \; {\red{\underline{{\underline{\pmb{\frak{ Side = 16 \; cm }}}}}}}$

$\dag$ Calculating the Total Surface Area :

$➢ \qquad \;$ TSA = 6 × Side²

$\\ ➢ \qquad \;$ TSA = 6 × 16²

$\\ ➢ \qquad \;$ TSA = 6 × 256

$\\ ➢ \qquad \; {\green{\underline{{\underline{\pmb{\frak{ TSA = 1536 \; {cm}^{2} }}}}}}}$

$\therefore \;$ Total Surface Area of the Cube is 1536 cm² .

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