Question

1. robyn made a solid figure with unit - cubes, as shown below. she added on more cubes on top of her figure without changing the length or the width. when she finished, the final figure was a large cube. = 1 unit cube how many more unit cubes did robyn add to her solid figure? a 216 b. 252 c. 125 d. 180

Explanation:

Step1: Determine side - length of base

Count the number of unit cubes along the length and width of the base figure. The length and width of the base have 6 unit cubes each.

Step2: Find side - length of large cube

Since the final figure is a large cube and the length and width are not changed, the side - length of the large cube is 6.

Step3: Calculate volume of large cube

The volume of a cube is $V = s^3$, where $s = 6$. So $V=6^3=216$.

Step4: Calculate volume of original figure

The original figure has a height of 1, length of 6 and width of 6. Its volume $V_{original}=6\times6\times1 = 36$.

Step5: Calculate number of added cubes

The number of added cubes is the volume of the large cube minus the volume of the original figure. So $216−36 = 180$.

Answer:

D. 180