Short Answer 
The volume of Shape 1 is calculated using the formula 1/3(l)(w)(h) resulting in 20, while Shape 2 uses 1/3(1/2 B H1)H2 to yield a volume of 10. Thus, Shape 1 is twice the volume of Shape 2, disproving Ali’s claim that it is three times larger.
Step 1: Understand the Volume Formula for Shapes
The volume of a shape can be calculated using specific formulas. For Shape 1, the formula is 1/3 * (length)(width)(height), which helps in determining the volume of a prism or pyramid. The dimensions need to be multiplied appropriately before applying the fraction to find the total volume.
- For Shape 1: Formula is 1/3(l)(w)(h)
- For Shape 2: Formula is 1/3(1/2 B H1)H2
Step 2: Calculate the Volumes
Now, we can substitute the given dimensions into the formulas to compute the volumes for Shape 1 and Shape 2. This involves careful multiplication and applying the fractional factor at the end. It is essential to follow the order of operations to avoid mistakes.
- For Shape 1: 1/3(4)(3)(5) = 20
- For Shape 2: 1/3(1/2 x 4 x 5)3 = 10
Step 3: Compare the Volumes and Address Misconceptions
After computing the volumes, it is critical to compare them accurately. We find that the volume of Shape 1 is 20, while Shape 2 has a volume of 10. This clearly shows that Shape 1 is twice as much as Shape 2 since 10 multiplied by 2 equals 20; hence, Ali’s statement of it being three times more is incorrect.
- Shape 1 Volume: 20
- Shape 2 Volume: 10
- Conclusion: 20 is twice as much as 10, not three times.