If the length of a diagonal of a cube is 12 root 3 cm find its surface area and volume

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Question

If the length of a diagonal of a cube is 12 root 3 cm find its surface area and volume

Spam answer will be reported :)​

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Eva 3 months 2021-07-24T12:54:44+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-24T12:56:27+00:00

    Answer:

    Given: Length of the diagonal of a cube is \sf 12 \sqrt{3} cm.

    To find: Surface area & Volume of cube?

    ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

    ☯ Let side of cube be a cm.

    ⠀⠀⠀⠀

    Now,

    \dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\

    Diagonal of cube is given by,

    \star\;{\boxed{\sf{\pink{Diagonal_{\:(cube)} = \sqrt{3} \times side}}}}\\ \\

    :\implies\sf 12 \sqrt{3} = \sqrt{3} \times \times a\\ \\ \\ :\implies\sf a =  \dfrac{12 \cancel{\sqrt{3}}}{ \cancel{\sqrt{3}}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{a = 12\:cm}}}}}\;\bigstar\\ \\

    \therefore\:{\underline{\sf{Length\:of\:Side\:of\:cube\:is\: {\textsf{\textbf{12\:cm}}}.}}}

    ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

    ⋆ Now, Finding Surface Area of cube,

    \star\;{\boxed{\sf{\pink{TSA_{\:(cube)} = 6 \times (side)^2}}}}\\ \\

    :\implies\sf TSA_{\:(cube)} = 6 \times (12)^2\\ \\ \\:\implies\sf TSA_{\:(cube)} = 6 \times 12 \times 12\\ \\ \\ :\implies\sf TSA_{\:(cube)} = 6 \times 144\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{TSA_{\:(cube)} = 864\:cm^2}}}}}\;\bigstar\\ \\

    \therefore\:{\underline{\sf{Surface\:area\:of\:cube\:is\: \bf{864\:cm^2}.}}}

    ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

    ⋆ Now, Volume of cube,

    \star\;{\boxed{\sf{\pink{Volume_{\:(cube)} = (side)^3}}}}\\ \\

    :\implies\sf Volume_{\:(cube)} = (12)^3\\ \\ \\ :\implies\sf Volume_{\:(cube)} = 12 \times 12 \times 12\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{Volume_{\:(cube)} = 1728\:cm^3}}}}}\;\bigstar\\ \\

    \therefore\:{\underline{\sf{Volume\:of\:cube\:is\: \bf{1728\:cm^3}.}}}

    0
    2021-07-24T12:56:42+00:00

    Answer :

    • The surface area of cube = 864cm²
    • The volume of cube = 1728cm³

    Step-by-step explanation:

    To Find:

    • The surface area of cube
    • The volume of cube

    Solution:

    Given that,

    • The length of a diagonal of cube is 123 cm.

    We know that,

    Diagonal of cube = a√3 units,

    Where,

    • a = side of cube.

    ∴ The side of cube :-

    a√3 = Diagonal of cube

    a√3 = 12√3

    a = 12cm.

    According the question,

    • The surface area of cube

    We know that,

    Surface area of cube = 6(a)² sq. units,

    ∴ The surface area is :-

    6(a)²

    6(12)²

    6 × 144

    864cm²

    • The volume of cube

    We know that,

    Volume of cube = (a)³ cubic units,

    ∴ The volume is :-

    (a)³

    (12)³

    ( 12 × 12 × 12 )

    ( 144 × 12 )

    1728cm³

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