Question

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

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Answer 1

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 12√3 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

Answer 2

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,

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

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

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