Verified answer

Answer:

Given :-

• A cube whose lateral surface area is 36 cm².

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To Find :-

• What is the edge of a cube.

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Formula Used :-

[tex]\clubsuit[/tex] Lateral Surface Area or L.S.A. Of Cube Formula :

[tex]\small \bigstar \: \: \sf\boxed{\bold{\pink{Lateral\: Surface\: Area_{(Cube)} =\: 4a^2}}}\: \: \: \bigstar\\[/tex]

where,

• a = Side or Edge

[tex]\\[/tex]

Solution :-

Let,

[tex]\mapsto \bf Edge_{(Cube)} =\: a\: cm\\[/tex]

Given :

• Lateral Surface Area or L.S.A. of Cube = 36 cm²

According to the question by using the formula we get,

[tex]\small \implies \bf Lateral\: Surface\: Area_{(Cube)} =\: 4a^2\\[/tex]

[tex]\implies \sf 36 =\: 4a^2[/tex]

[tex]\implies \sf \dfrac{36}{4} =\: a^2[/tex]

[tex]\implies \sf 9 =\: a^2[/tex]

[tex]\implies \sf \sqrt{9} =\: a[/tex]

[tex]\implies \sf 3 =\: a[/tex]

[tex]\implies \sf\bold{\blue{a =\: 3}}\\[/tex]

Hence, the required edge of a cube is :

[tex]\dashrightarrow \sf Edge_{(Cube)} =\: a\: cm\\[/tex]

[tex]\dashrightarrow \sf\bold{\red{Edge_{(Cube)} =\: 3\: cm}}\\[/tex]

[tex]\sf\bold{\purple{\underline{\therefore\: The\: edge\: of\: a\: cube\: is\: 3\: cm\: .}}}\\[/tex]

[tex]\\[/tex]

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