Question

The volume of a cube is 1728 cm^3. Find its total surface area​

Answer 1

Answer :

≫ The Total surface area of cube is 864 cm².

Given :

• The volume of a cube is 1728 cm³.

To Find :

• Total Surface Area of cube = ?

Solution :

★ Finding the Length of the side of cube :

→ Volume of cube = (Length)³

→ 1728 = (Length)³

Taking cube root to both the sides we get :

→ ∛1728 = Length

→ 12 cm = Length

→ Length = 12 cm

• Hence,the length of the side of cube is 12 cm.

★ Now,let's find the Total Surface Area of cube :

→ TSA of cube = 6 × (Length)²

→ TSA of cube = 6 × (12)²

→ TSA of cube = 6 × 144

→ TSA of cube = 864 cm²

• Hence, the TSA of cube is 864 cm².

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★ Formulas related to cube and cuboid :

• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³

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Answer 2

Given:-

• Volume of a cube is 1728 cm³.

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To find:-

• Total surface area of cube?

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Solution:-

★ Using Formula:-

$\star{\boxed{\sf{\orange{Volume~ of~ cube = (Length)^3}}}}$

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※ Firstly, find the length of cube:-

$\large{\tt{\longmapsto{1728 = (Length)^3}}}$

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$\large{\tt{\longmapsto{\sqrt[3]{1728} = Length}}}$

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$\boxed{\large{\tt{\longmapsto{\green{Length = 12~ cm}}}}}$

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Hence, the length of cube is 12 cm.

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※ Finding the TSA of cube:-

$\large{\tt{\longmapsto{6 = (Length)^3}}}$

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$\large{\tt{\longmapsto{6 = (12)^3}}}$

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$\large{\tt{\longmapsto{6 = 144}}}$

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$\boxed{\large{\tt{\longmapsto{\red{864 cm^2}}}}}$

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Hence, the total surface area of cube is 864 cm².

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