A cube has edge 2 cm and a cuboid has dimensions 1 cm × 2 cm × 3 cm. Paint available covers 54 cm^2. Which can be fully painted?

Introduction / Context:
This is a budgeted-area problem: determine whether available paint is sufficient to cover the total surface areas. Compute each object’s required area and compare with the available coverage. The twist is checking if both together still fit the paint budget.

Given Data / Assumptions:

• Cube edge a = 2 cm ⇒ S_cube = 6a^2 = 6 * 4 = 24 cm^2.
• Cuboid 1 × 2 × 3 ⇒ S_cuboid = 2(ab + bc + ca) = 2(2 + 6 + 3) = 22 cm^2.
• Available area = 54 cm^2.

Concept / Approach:
Sum the two required areas and compare with 54. If the sum ≤ 54, both can be painted; otherwise determine which individual one(s) fit.

Step-by-Step Solution:
S_cube = 24 cm^2S_cuboid = 22 cm^2Total needed = 24 + 22 = 46 cm^2 ≤ 54 cm^2Hence both can be painted fully.

Verification / Alternative check:
Individually each requires less than 54; together they still use only 46, leaving an 8 cm^2 margin.

Why Other Options Are Wrong:
“Only cube” or “Only cuboid” underestimate the available paint; “Neither” is false because 24 and 22 are both below 54.

Common Pitfalls:
Forgetting to double for the cuboid’s opposite faces; arithmetic slips in 2(2 + 6 + 3).

Final Answer:
Both cube and cuboid can be painted