Question

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

• A. 25
• B. 16
• C. 20
• D. 18

Hint:

Only the freshly cut face is unpainted; find its area as a fraction of the total surface area of one new block.

Answer 1

The Correct Option is A

Step 1: Pick a convenient cube size.
Take s = 4 cm.

Step 2: Size of each new block.
Each block measures 4 x 4 x 2 cm.

Step 3: Total surface area of one block.
TSA = 2(4x4 + 4x2 + 2x4) = 2(16+8+8) = 64 cm^2

Step 4: Unpainted area.
The cut creates one new face on each block, of size 4x4=16 cm^2, the only unpainted face.

Step 5: Fraction unpainted.
16/64 x 100 = 25%

Final Answer: 25 percent of each block's surface is unpainted.