Question

The volume of a cube is 729 cm3. Find its surface area ​

Answer 1

Answer:

486cm²

Step-by-step explanation:

Volume of a cube = a³

= 729 cm³

so, a = 9 cm

surface area of a cube = 6a²

= 6×(9)²

= 6 × 81

= 486cm²

Answer 2

Given

• Volume of a cube is 729 cm³.

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To find

• Surface area of the cube.

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Solution

• Let the each edge of the cube be a.
• We have volume of the cube and need to find its surface area.

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☆ Firstly, we have to find the length of each side of the cube.

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$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {Using\: Formula}$

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$\dag{\boxed{\boxed{\bf{Volume_{(Cube)} = a^3}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Volume = 729}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a^3 = 729}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a = \sqrt[3]{729}}$

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$\frac:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{a = 9}}}}$

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• Now, we have each side of the cube.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{As\: we\: know}}}$

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$\dag{\boxed{\boxed{\bf{TSA_{(Cube)} = 6a^2}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {TSA = 6a^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {TSA = 6 \times (9)^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {TSA = 6 \times 81}$

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$\frak:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{TSA = 486\: cm^2}}}}$

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Hence,

• Surface area of the cube is 486cm².