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Challenge Sraw 2 different cuboids with a total volume of \( 40 \mathrm{~m}^{3} \), writing the dimensions, Your drawings don't need to be to scalel

Ask by Higgins Todd. in Turkey
Feb 02,2025

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Here are two different cuboids with a total volume of \(40\, \mathrm{m}^{3}\): --- **Cuboid 1:** - **Dimensions:** 5m (Length) × 2m (Width) × 2m (Height) - **Volume:** 20\, \mathrm{m}^{3} **Cuboid 2:** - **Dimensions:** 4m (Length) × 2m (Width) × 2.5m (Height) - **Volume:** 20\, \mathrm{m}^{3} **Total Volume:** 40\, \mathrm{m}^{3} --- These cuboids have different dimensions but together they occupy a total volume of \(40\, \mathrm{m}^{3}\).

Solution

Sure, I'd be happy to help with that! Below are two different cuboids whose volumes sum up to \(40\, \mathrm{m}^{3}\). I'll provide their dimensions and simple ASCII drawings to illustrate their shapes. Please note that the drawings are not to scale. --- ### **Cuboid 1** **Dimensions:** - **Length (L):** 5 meters - **Width (W):** 2 meters - **Height (H):** 2 meters **Volume Calculation:** \[ \text{Volume} = L \times W \times H = 5\, \text{m} \times 2\, \text{m} \times 2\, \text{m} = 20\, \mathrm{m}^{3} \] **ASCII Drawing:** ``` +-----------+ | | | | 2m | | +-----------+ 5m ``` *Top View:* ``` +-----------+ | | | | +-----------+ 5m x 2m ``` --- ### **Cuboid 2** **Dimensions:** - **Length (L):** 4 meters - **Width (W):** 2 meters - **Height (H):** 2.5 meters **Volume Calculation:** \[ \text{Volume} = L \times W \times H = 4\, \text{m} \times 2\, \text{m} \times 2.5\, \text{m} = 20\, \mathrm{m}^{3} \] **ASCII Drawing:** ``` +-----------+ | | | | 2.5m | | +-----------+ 4m ``` *Top View:* ``` +-----------+ | | | | +-----------+ 4m x 2m ``` --- ### **Total Volume** \[ \text{Total Volume} = 20\, \mathrm{m}^{3} + 20\, \mathrm{m}^{3} = 40\, \mathrm{m}^{3} \] --- Feel free to adjust the dimensions as needed, as there are infinitely many combinations of lengths, widths, and heights that can give you a total volume of \(40\, \mathrm{m}^{3}\). Let me know if you need further assistance or more examples!

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One possible cuboid could have dimensions of \( 2 \mathrm{~m} \times 5 \mathrm{~m} \times 4 \mathrm{~m} \). This calculates to a volume of \( 2 \times 5 \times 4 = 40 \mathrm{~m}^{3} \). You can imagine it as a rectangular box that’s wide and not too tall. Another cuboid might have dimensions of \( 1 \mathrm{~m} \times 10 \mathrm{~m} \times 4 \mathrm{~m} \). The volume here is \( 1 \times 10 \times 4 = 40 \mathrm{~m}^{3} \) as well. Picture a long, thin box that stretches out horizontally. Each of these cuboids showcases how different dimensions can still yield the same volume!

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