Question

The figure shown below is a composition of cubes of four by four matrix. Some of the cubes are removed, but no cubes that are not visible are removed. How many cubes are there in the whole composition? 

• A. 45
• B. 47
• C. 49
• D. 51

Hint:

When counting cubes in a matrix, consider the total number before removing any cubes and then subtract the visible missing cubes.

Answer 1

The Correct Option is C

Step 1: Understanding the composition.
The composition is based on a 4x4 matrix, so the total number of cubes before any cubes are removed is: \[ 4 \times 4 \times 4 = 64 \, \text{cubes}. \] However, some cubes are missing from the visible view, as shown in the diagram. By counting the missing cubes, we determine the correct total.
Step 2: Analysis of options.
- (A) 45: This is not the correct answer, as it underestimates the number of cubes.
- (B) 47: This is too few to account for all the missing cubes.
- (C) 49: This is the correct answer, considering the number of missing cubes.
- (D) 51: This is too many cubes to be consistent with the given image.

Step 3: Conclusion.
Thus, the correct answer is (C) 49.