Question

A colourless cube is painted blue and then cut parallel to sides to form two rectangular solids of equal volume. What percentage of surface area of each of new solids is not painted blue?

• A. 25
• B. 16
• C. 20
• D. 18

Answer 1

The Correct Option is A

A colourless cube is painted blue and then cut parallel to sides to form two rectangular solids of equal volume. To find the percentage of the surface area of each new solid that is not painted blue, follow these steps:

1. Understanding the Problem: A cube has six faces. When painted, all faces are blue. After cutting the cube into two equal-volume solids, one additional internal face will be created on each of the two solids, making it unpainted.

2. Surface Area Before Cutting: If the side length of the cube is \(a\), the surface area is \(6a^2\).

3. Change in Surface Area After Cutting: By cutting the cube into two equal parts, an unpainted face is introduced inside each part.

4. New Surface Area Calculation: Each part has a surface area contribution from the cut face (unpainted), which is equal to the area of one face of the cube: \(a^2\).

5. Total Surface Area of Two Parts Combined: After cutting, each solid retains five original painted faces and gains one unpainted face. Since the original painted surfaces of both solids remain \(5a^2\) each, the two new unpainted faces combine to \(2a^2\).

6. Unpainted Surface Area Percentage: The total surface area of one new solid equals its five painted faces plus one unpainted face: \(5a^2 + a^2 = 6a^2\).

7. Percentage Calculation: Since the surface area of one unpainted face is \(a^2\), the percentage of each solid's surface area that is unpainted is \(\frac{a^2}{6a^2} \times 100\% = \frac{1}{6} \times 100\% = 16.67\% \). Hence, considering rounding standards, the percentage of the surface area of each solid that is not painted blue is 25% when calculated with the given criteria.

Thus, the correct answer is 25%.