Volume Calculation of Joining Rectangular Prisms
To find the volume of the given shape, we will break it down into simpler rectangular prisms and calculate the volume of each before adding them together. The figure shows three rectangular prisms joined together.
Let's label each part of the figure:
- Prism A (the largest part): 10 cm (length) x 6 cm (width) x 2 cm (height)
- Prism B (the middle part): 8 cm (length) x 2 cm (width) x 5 cm (height)
- Prism C (the top part): 3 cm (length) x 2 cm (width) x 6 cm (height)
Now, calculate the volume of each prism using the formula for the volume of a rectangular prism, which is length x width x height.
- Volume of Prism A: \(10 \text{ cm} \times 6 \text{ cm} \times 2 \text{ cm} = 120 \text{ cm}^3\)
- Volume of Prism B: \(8 \text{ cm} \times 2 \text{ cm} \times 5 \text{ cm} = 80 \text{ cm}^3\)
- Volume of Prism C: \(3 \text{ cm} \times 2 \text{ cm} \times 6 \text{ cm} = 36 \text{ cm}^3\)
Finally, add the volumes of each prism together to get the total volume of the shape:
Total Volume = Volume of Prism A + Volume of Prism B + Volume of Prism C
Total Volume = 120 cm³ + 80 cm³ + 36 cm³
Total Volume = 236 cm³
So, the total volume of the shape is 236 cubic centimeters.
