Question
Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall.
What is the number of cubes needed to fill this prism?
(1 point)
Responses
20 cubes
20 cubes
35 cubes
35 cubes
36 cubes
36 cubes
42 cubes
What is the number of cubes needed to fill this prism?
(1 point)
Responses
20 cubes
20 cubes
35 cubes
35 cubes
36 cubes
36 cubes
42 cubes
Answers
GPT-4o mini
To find the total number of cubes needed to fill the prism, we can break it down into two parts: the base and the column.
1. **Calculate the volume of the base:**
- The base is a rectangular prism that is 3 units long, 2 units wide, and 1 unit tall (since the standard size of a cube is 1 unit).
- The volume of the base = length × width × height = 3 × 2 × 1 = 6 cubes.
2. **Calculate the volume of the column:**
- The column is 1 cube wide, 1 cube deep, and 7 cubes tall.
- The volume of the column = 1 × 1 × 7 = 7 cubes.
3. **Total number of cubes:**
- Total cubes = volume of the base + volume of the column = 6 + 7 = 13 cubes.
Since the options provided do not include 13 cubes, it appears I might have misinterpreted the dimensions given in the problem.
If we consider if the column sits on top of the base, and needs to be added to the number of cubes filling up to a height of 7 cubes while spanning 3x2 in base:
1. The total volume of the prism would actually be the total volume at full height, which is also considered only for the cumulative height.
- If the base fills entirely to meet the column height, that is 3 × 2 × 7 = 42 units.
Finally:
- The full volume of the prism is 42 cubes.
**Answer: 42 cubes.**
1. **Calculate the volume of the base:**
- The base is a rectangular prism that is 3 units long, 2 units wide, and 1 unit tall (since the standard size of a cube is 1 unit).
- The volume of the base = length × width × height = 3 × 2 × 1 = 6 cubes.
2. **Calculate the volume of the column:**
- The column is 1 cube wide, 1 cube deep, and 7 cubes tall.
- The volume of the column = 1 × 1 × 7 = 7 cubes.
3. **Total number of cubes:**
- Total cubes = volume of the base + volume of the column = 6 + 7 = 13 cubes.
Since the options provided do not include 13 cubes, it appears I might have misinterpreted the dimensions given in the problem.
If we consider if the column sits on top of the base, and needs to be added to the number of cubes filling up to a height of 7 cubes while spanning 3x2 in base:
1. The total volume of the prism would actually be the total volume at full height, which is also considered only for the cumulative height.
- If the base fills entirely to meet the column height, that is 3 × 2 × 7 = 42 units.
Finally:
- The full volume of the prism is 42 cubes.
**Answer: 42 cubes.**