Question

the volume of cube is 216 cm square. find its tsa

Answer 1

Correct Question

• The volume of cube is 216 cm³. Find its total surface area.

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Given

• Volume of a cube is 216 cm³.

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To find

• Total surface area of the cube.

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Solution

• Here, we have volume of a cube.

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

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

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Here,

• a = edge of the cube

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$\tt:\implies\: \: \: \: \: \: \: \: {a^3 = 216}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a = \sqrt[3]{216}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {a = 6\: cm}$

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• Now, we have each edge of the cube.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Finding\: TSA\: of\: cube}}}$

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

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

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$\tt:\implies\: \: \: \: \: \: \: \: {TSA = 6 \times 36}$

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$\tt:\implies\: \: \: \: \: \: \: \: {TSA = 216\: cm^2}$

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Hence,

• Total surface area of the cube is 216cm².

Answer 2

Appropriate question :

• The volume of cube is 216 cm square. Find its total surface area.

Given :

• Volume of cube is 216 cm square.

To Find

• Surface area of cube = ?

Solution :

➠ Surface area of cube = 6a²

➠ 216 (Surface area of cube) = 6a²

➠ Surface area = 6 cm..

Now, according to the question,

Formula used :

• Volume of cube = area × area × area

Putting the values,

➨ 6cm × 6cm × 6cm

➨ 216 cm³

Therefore,

• The surface area of cube is 216cm³