Question

the total surface area of a solid cube is 96cm^2. find the edge of the cube​

Answer 1

Given that,

• Total surface area of a solid cube is 96 cm².

Let the edge of the cube be a cm.

⠀

$\dag\;{\underline{\frak{As \ We \ know \ that,}}}$⠀

$\star\:\boxed{\sf{\pink{TSA_{\:(Total \: surface \: area)} = 6(a)^2}}}$

⠀

Therefore,

⠀⠀⠀⠀

$:\implies\sf 6a^2 = 96 \\\\\\:\implies\sf a^2 = \cancel\dfrac{96}{6} \\\\\\:\implies\sf a^2 = 16\\\\\\:\implies\sf a = \sqrt{16}\\\\\\:\implies{\underline{\boxed{\frak{\pink{a = 4 \ cm}}}}}\:\bigstar$

⠀

$\therefore\:{\underline{\sf{Hence, \ edge \ of \ cube \ is \ \bf{4 \ cm}.}}}$⠀⠀⠀

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\qquad\qquad{\underline{\underline{\bigstar\: \bf\:Formulaes \ related \ to \ it \: :}}}$⠀⠀

• Curved surface area of cube = 4a²
• Total surface area of cube = 6a²
• Volume of cube = a³
• Curved surface area of cuboid = 2(l + b)h
• Total surface area cuboid = 2(lb + bh + hl)
• Volume of cuboid = l × b × h

Answer 2

Answer:

Given :-

• The total surface area of a cube is 96 cm².

To Find :-

• What are the edges of the cube.

Formula Used :-

$\sf\boxed{\bold{\large{T.S.A\: of\: cube\: =\: 6{(a)}^{2}}}}$

where,

• a = Side or edge.

Solution :-

Let, the edge of the cube be a

Given :

• T.S.A of cube = 96 cm²

According to the question by using the formula we get,

⇒ $\sf 96\: =\: 6{(a)}^{2}$

⇒ $\sf \dfrac{96}{6} =\: {a}^{2}$

⇒ $\sf \dfrac{\cancel{96}}{\cancel{6}} =\: {a}^{2}$

⇒ $\sf 16 =\: {a}^{2}$

⇒ $\sf \sqrt{16} =\: a$

⇒ $\sf 4 =\: a$

➠ $\sf\bold{\red{a =\: 4\: cm}}$

$\therefore$ The edge of the cube is 4 cm .