How can you make three different rectangular prisms using 18 one-centimeter cubes? Give the length, width, and height of each prism.
18 x 1 x 1
9 x 2 x 1
3 x 3 x 2
This was so helpful I am going to get an A on my assighnment!
Well, if you're feeling a bit "cubey," here are three prism possibilities that will make geometry a breeze:
1. The "Almost Square": You can create a rectangular prism with dimensions 3 cm x 3 cm x 2 cm. It's not perfectly square, but it's close enough to pass as a hipster's idea of a square!
2. The "Lofty Leprechaun": Another option is a prism with dimensions 2 cm x 6 cm x 0.5 cm. This prism may be a bit on the thin side, but hey, it's perfect for mischievous leprechauns who need places to hide their gold!
3. The "Long & Lean": Lastly, you can make a prism with dimensions 1 cm x 9 cm x 2 cm. This one is a real stretch, but sometimes in life, it's good to be long and lean. Just ask any stretchy toy!
Remember, while these may not be conventional prisms, they'll certainly add a touch of quirkiness to your geometric creations!
To make three different rectangular prisms using 18 one-centimeter cubes, we need to consider the dimensions of each prism. Let's go through each possibility step by step:
Prism 1:
- The length, width, and height of this prism should be factors of 18.
- Let's start with a length of 6 cm, a width of 3 cm, and a height of 1 cm.
- This arrangement would use 6 cubes, as (6 x 3 x 1 = 18).
Prism 2:
- Since we have already used 6 cubes, we have 12 remaining cubes.
- Let's try a length of 4 cm, a width of 3 cm, and a height of 1 cm.
- This arrangement would use 12 cubes, as (4 x 3 x 1 = 12).
Prism 3:
- Now, we have 6 cubes left.
- Let's try a length of 3 cm, a width of 2 cm, and a height of 1 cm.
- This arrangement would use 6 cubes, as (3 x 2 x 1 = 6).
So, we have three different rectangular prisms:
Prism 1: Length = 6 cm, Width = 3 cm, Height = 1 cm
Prism 2: Length = 4 cm, Width = 3 cm, Height = 1 cm
Prism 3: Length = 3 cm, Width = 2 cm, Height = 1 cm
To solve this problem, we need to find three different combinations of length, width, and height that result in a total of 18 one-centimeter cubes.
Here's how we can approach it:
1. Start with a prism with the smallest possible dimensions: 1 cm by 1 cm by 1 cm. This uses up 1 cube, leaving us with 17 cubes remaining.
2. Next, we can try increasing one of the dimensions while keeping the others constant to see if we can use up more cubes. Let's try increasing the length to 2 cm while keeping the width and height as 1 cm. This uses up an additional 2 cubes, leaving us with 15 cubes remaining.
3. Now, let's try increasing the width to 2 cm while keeping the length and height as 1 cm. This uses up another 2 cubes, leaving us with 13 cubes remaining.
4. Finally, let's try increasing the height to 2 cm while keeping the length and width as 1 cm. This uses up another 2 cubes, leaving us with 11 cubes remaining.
By following this approach, we have found three different rectangular prisms using 18 one-centimeter cubes:
- Prism 1: Length = 1 cm, Width = 1 cm, Height = 1 cm.
- Prism 2: Length = 2 cm, Width = 1 cm, Height = 1 cm.
- Prism 3: Length = 1 cm, Width = 2 cm, Height = 1 cm.
Remember, there may be other possible combinations as well, so feel free to explore further if you're interested in finding more solutions.