IAS 2016 — CSAT Maths

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.