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The accompanying image shows a large cube made of dark and white small sugar cubes. Small cubes of the diagonally arranged row of the bottom surface of the large cube, small cubes of the row with one face on the right-hand surface of the large cube, small cubes of the row with one face on the front surface of the large cube, and small cubes of the column with one face on the top of large cube surface are all dark. Select the number of small white cubes of the large cube.

The accompanying image shows a large cube made of dark and white small sugar cubes. Small cubes of the diagonally arranged row of the bottom surface of the large cube, small cubes of the row with one face on the right-hand surface of the large cube, small cubes of the row with one face on the front surface of the large cube, and small cubes of the column with one face on the top of large cube surface are all dark. Select the number of small white cubes of the large cube. Correct Answer 49

The total number of the small cubes will be 43 = 64.

Let's count the dark cubes separately for the given figure step by step:

i) Small cubes of the diagonally arranged row of the bottom surface of the large cube

[ alt="F1 Savita Engineering 23-4-22 D2" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D2.png" style="width: 158px; height: 187px;">       [ alt="F1 Savita Engineering 23-4-22 D6" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D6.png" style="width: 145px; height: 251px;">

Thus we can say there is a total of 4 Dark cubes.

ii) small cubes of the row with one face on the right-hand surface of the large cube

[ alt="F1 Savita Engineering 23-4-22 D4" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D4.png" style="width: 237px; height: 111px;">

This arrangement has a total of 4 dark cubes.

iii) small cubes of the row with one face on the front surface of the large cube

[ alt="F1 Savita Engineering 23-4-22 D3" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D3.png" style=" width: 113px; height: 173px;">

This arrangement has a total of 4 dark Cubes.

iv) small cubes of the column with one face on the top of the large cube surface are all dark.

[ alt="F1 Savita Engineering 23-4-22 D5" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D5.png" style="width: 137px; height: 183px;">[ alt="F1 Savita Engineering 23-4-22 D7" src="//storage.googleapis.com/tb-img/production/22/04/F1_Savita__Engineering_23-4-22_D7.png" style="width: 179px; height: 263px;">

Thus we can say this arrangement has a total of 3 cubes only because one cube is common in the small cubes of the row with one face on the right-hand surface of the large cube which is already counted in step number 2.

Thus the total number of dark cubes = 4 + 4 + 4 + 3 = 15.

Thus the total number of the white cube of the larger cube will be:
⇒ Total number of the small cube - Total number of the dark cubes
⇒ 64 - 15
⇒ 49
Hence, the correct answer is "49".

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