Question - Calculating the Volume of a Composite Solid
Solution:
To find the volume of this composite solid, we need to break it into smaller parts whose volumes we can calculate easily and then sum up those volumes. By looking at the shapes, we can split the figure into two rectangular prisms.Let's call the one on the left "Prism A" and the one on the right "Prism B".1. **Volume of Prism A**: For Prism A, we have the dimensions 2 cm by 6 cm by 10 cm. The volume (V) of a rectangular prism can be found using the formula V = length × width × height. Therefore, V of Prism A = 2 cm × 6 cm × 10 cm = 120 cm³.2. **Volume of Prism B**: For Prism B, the dimensions are not as straightforward, so we need to calculate the missing dimensions first. We can see that the height of the prism is 5 cm. The length of the prism B can be determined by subtracting the length of prism A from the total length. That is 10 cm (total length) - 6 cm (length of A) = 4 cm. So, the length of prism B is 4 cm. The width of prism B is the total width, which is 8 cm. Therefore, V of Prism B = 5 cm × 4 cm × 8 cm = 160 cm³.Now, we add the volumes of the two prisms together:Total Volume = Volume of Prism A + Volume of Prism BTotal Volume = 120 cm³ + 160 cm³ = 280 cm³.The volume of the composite solid is 280 cm³.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com