Question

The surface area of a cubical box is 486 CM square find the length of an edge of this box

Answer 1

$\underline{\bold{\footnotesize{Given:}}} \\ \\Total\:surface\:area = 486{cm}^{2} \\ \\ \underline{\bold{\footnotesize{To\:Find:}}} \\ \\ Length\:of\:each\:side . \\ \\ Let\:the\:Side\:be\:S. \\ \\ \bold{We\:know\:that,}\\ \\ \boxed{\bold{Total\:Surface\:Area=6\times {side}^{2}}} \\ \\ \bold{According\:to\:the\:question,} \\ \\ Total\:surface\:area = 486{cm}^{2} \\ \\ \implies\bold{486{cm}^{2} = 6\times {s}^{2}} \\ \\ \implies\bold{\dfrac{486}{6}{cm}^{2} ={s}^{2}} \\ \\ \implies\bold{81{cm}^{2} = {s}^{2}} \\ \\\implies\bold{9cm = side} \\ \\ \boxed{\bold{Side =9cm}}$

The length of each side is 9cm.

Answer 2

Answer:

⇒ x = 9 cm

Step-by-step explanation:

Let the Total Surface Area be x cm

we know that,

Surface area of a cube= 6 (side)²

According to Question,

Total surface area = 486 cm² (given)

⇒6 × s²=486 cm²

⇒ 6 × x² = 486  

⇒ 6x² = 486  

let shift 6 to Right hand side

⇒ x² = 486 / 6  

let find the square root of the number

⇒ x² = 81  

⇒ x = 9

hence, the edge of this box is 9 cm