Question

From each face of the given cube, an unit cube (shaded) is cut out. What will be the surface area of the remaining portion of the cube (in cm2)?


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Answer 1

Given,

A big cube, unit cubes cut out from the faces

To find,

The surface area of the remaining portion

Solution,

Since the sides of cubes are not given, let the sides of the Cube be A and of a unit cube be a.

So,

The surface area of Cube = 6 (side)²

= 6 × A²

= 6A² cm²

The surface area of unit cube = 6(a)²

= 6a² cm²

Since there are 6 faces of the unit cube,

The surface area of 6 unit cubes = 6 × 6a²

= 36a² cm²

Now,

the remaining portion of the cube = Surface area of Cube - 6×surface area of the unit cube

= 6A² - 36a²

= 6(A² - 6a²) cm²

Here you can put values of A and a according to the value given in the question.

Therefore the surface area of the remaining portion of the cube is 6(A²-6a²) cm².