A piece of tin is in the form of a rectangle having length 12cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:

Correct Option (C)

The area of the rectangular piece of tin is determined by multiplying its length and width. Given the length as 12 cm and the width as 8 cm, the area of the tin is 12 cm × 8 cm = 96 cm².

When this rectangular tin is utilized to construct a closed cube, the total surface area of the cube must correspond to the area of the tin sheet. The formula for the total surface area of a closed cube with side 'a' is 6a².

Equating the area of the tin sheet to the surface area of the cube:

$$6a^{2} = 96$$6a2=96

To find the side 'a', we solve the equation:

$$a^{2} = \frac{96}{6}$$a2=696​

$$a^{2} = 16$$a2=16

$$a = \sqrt{16}$$a=16​

$$a = 4 \text{ cm}$$a=4 cm

Therefore, the side of the constructed cube is 4 cm.

Incorrect Options:

The side of the cube must yield a total surface area of 96 cm² to be consistent with the area of the tin sheet.

• If the side of the cube were 2 cm (Option A), its total surface area would be $6 \times (2 \text{ cm})^{2} = 6 \times 4 \text{ cm}^{2} = 24 \text{ cm}^{2}$6×(2 cm)2=6×4 cm2=24 cm2, which does not match the available tin area of 96 cm².
• If the side of the cube were 3 cm (Option B), its total surface area would be $6 \times (3 \text{ cm})^{2} = 6 \times 9 \text{ cm}^{2} = 54 \text{ cm}^{2}$6×(3 cm)2=6×9 cm2=54 cm2, which is not equal to 96 cm².
• If the side of the cube were 6 cm (Option D), its total surface area would be $6 \times (6 \text{ cm})^{2} = 6 \times 36 \text{ cm}^{2} = 216 \text{ cm}^{2}$6×(6 cm)2=6×36 cm2=216 cm2, which significantly exceeds the available tin area of 96 cm².