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: Set up the cube.
Let the side of the cube be s. Since the whole cube is painted first, every one of its 6 outer faces is blue before any cut is made.

Step 2: Understand the cut.
The cube is cut parallel to a pair of faces into two rectangular solids of equal volume, so the cut passes exactly through the middle. Each new solid has dimensions s x s x s/2. The cut face is new surface, never painted.

Step 3: Total surface area of one new solid.
TSA = 2(s.s + s.(s/2) + (s/2).s) = 2(s^2 + s^2/2 + s^2/2) = 4s^2

Step 4: Unpainted area.
Only the newly cut face, area s^2, is unpainted.

Step 5: Percentage.
s^2 / 4s^2 x 100 = 25%

Final Answer: 25 percent of the surface area of each new solid is not painted blue.