Question

A large cube has side-length 7cm. On each of its 6 faces, the two diagonals are drawn in
red. The large cube is then cut into small cubes with side-length 1cm. How many small
cubes will have at least one red line drawn on it?
(A) 54
(D) 78
(C) 70
(B) 62
(E) 86

Answer 1

Answer:

B: 62

This is the correct answer

Answer 2

Concept

a cube could be a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

Given

We are given a cube with side length $7cm$. Diagonals of red color are drawn on each faces and so large cube is take away small cubes with side length $1cm.$

Find

We have to search out the amount of small cubes will have a minimum of one line drawn on that.

Solution

Since the length of an outsized cube is $7cm$.

So, the amount of an oversized cube is $7\times 7\times 7=343cm^3$

Since the tiny cubes with $1cm$ side lengths.

So, a tiny low cube volume is $1\times 1\times 1=1cm^3$.

Hence, the big cube are often divided by $\frac{343cm^3}{1cm^3}=343$ small cubes.

Since for every sides there are two red diagonals for every side.

There are $7\times2-1=13$ cubes with a minimum of line drawn.

And we know that a cubes has six faces.

Thus, $13\times 6=78$ cubes with a minimum of one line drawn.

Hence, option D is correct.

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