Question

Find the edge of the cube if the total surface area of a cube is 96 cm​2​​.

Answer 1

Answer:

4

Step-by-step explanation:

6a³ is the total surface area of the cube

so,

6a²= 96

a²= 16

a = 4

Answer 2

Given :

• Total surface area of a cube = 96 cm²

To Find :

• The Edge of the cube

Solution :

Total surface area (TSA) of a cube is given by ,

$\\ \star \: {\boxed{\purple{\sf{TSA_{(cube)} = 6 {a}^{2} }}}}$

Here ,

• a is the edge of the cube

Substituting the values we have in the formula ,

$\\ : \implies \sf \: 96 \: = 6 {a}^{2}$

$\\ : \implies \sf \: {a}^{2} = \frac{96}{6}$

$\\ : \implies \sf \: {a}^{2} = 16$

$\\ : \implies \sf \: a = \sqrt{16}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{a = 4 \: cm}}}}} \: \bigstar$

$\\ \therefore{\underline{\sf{Hence \: , \: The \: edge \: of \: the \: given \: cube \: is \: \bold{4 cm}}}}$