Now, to find the area of the metal required for the five faces (excluding the lid), use the formula for the area of a square: \( \text{Area} = s^2 \times \text{number of faces} \).
The number of faces without the lid is 5, so the area of the metal required is \(5 \times 6^2 = 5 \times 36 = 180\) square centimeters.
Answers & Comments
[tex]Let \: the \: side \: of \: a \: cube \: is \\ \\ = \: a \: \: cm[/tex]
[tex]Given \: volume \: of \: a \: cube \: is \\ \\ = 216 \: {cm}^{3} [/tex]
[tex] {a}^{3} = 216 \\ \\ a = \sqrt[3]{216} \\ \\ a = \sqrt{6 \times 6 \times 6} \\ \\ a = 6 \: cm[/tex]
[tex]Surface \: area \: of \: cube \: is \\ \\ = 6 {a}^{2} \\ \\ = 6( {6)}^{2} \\ \\ = 6(36) \\ \\ = 216 \: {cm}^{2} [/tex]
Answer:
To find the area of the metal required for a cubical base without a lid, we need to understand that a cube has six identical square faces.
Let the side of the cube be \(s\). Given that the volume of the cube is 216 cm³, the formula for the volume of a cube is \( \text{Volume} = s^3 \).
So, \(s^3 = 216\).
To find the side length (\(s\)), take the cube root of 216:
\(s = \sqrt[3]{216}\)
\(s = 6\) cm (since \(6 \times 6 \times 6 = 216\))
Now, to find the area of the metal required for the five faces (excluding the lid), use the formula for the area of a square: \( \text{Area} = s^2 \times \text{number of faces} \).
The number of faces without the lid is 5, so the area of the metal required is \(5 \times 6^2 = 5 \times 36 = 180\) square centimeters.