Question

find the measure of the diagonal of a cube if its total surface area is 18 cm square​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Total surface area of cube is 18 sq. cm.

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Diagonal of cube

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We know that ,

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$\underline{\bold{\texttt{Total surface area of cube :}}}$

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➠ 6s²

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Where ,

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• s = Side of cube

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$\rm{ \large{\pink{\underline\blue{According \: to \: the \ question :}}}}$

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Total surface area of cube is 18 sq. cm.

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So,

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➜ 6s² = 18

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➜ s² = 18/6

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➜ s² = 3

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➨ s = √3 ⚊⚊⚊⚊ ⓵

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• Hence the side of cube is 3 cm

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$\underline{\bold{\texttt{Diagonal of cube :}}}$

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➠ √3 × s

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Where ,

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• s = Side of cube

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From ⓵ we got that side of given cube is √3 cm

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Thus , the diagonal of cube is

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➜ √3 × √3

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➨ 3 cm.

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• Hence the diagonal of cube is 3 cm

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Additional information

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Volume of cube

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• $\sf s ^3$

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Where,

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➻ s = Side

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Properties of cube

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• It has all its faces in a square shape

• All the faces or sides have equal dimensions

• The plane angles of the cube are the right angle

• Each of the faces meets the other four faces

• Each of the vertices meets the three faces and three edges