A cube of side 5 cm has been assembled using 125 cubes each of 1 cm edge. One cube is removed from the middle of each of the faces of the cube. What is the surface area (in cm²) of the remaining solid?

Correct option is D

Given:

Side of the larger cube (a) = 5 cm

Side of each smaller cube (b) = 1 cm

Formula Used:

Surface area of a cube = 6 × (side)²

Change in surface area when one cube is removed:

ΔA = 5 × (side length of the smaller cube)² - 1 × (side length of the smaller cube)²

ΔA = 4 × (side length of the smaller cube)²

Solution:

Surface area of the larger cube = 6a² = 6 × 5² = 6 × 25 = 150 cm²

Increase in surface area when one cube is removed:

ΔA = 4 × (1 cm)² = 4 cm²

Total increase = 6 × ΔA = 6 × 4 cm² = 24 cm²

Overall surface area of the remaining solid = Original surface area + Total increase in surface area

Overall surface area of the remaining solid=150 cm² + 24 cm² = 174 cm²