Given:
A combined figure of a triangular prism and a cuboid.
To find:
The volume of the finished object assuming it is empty inside.
Solution:
From the given figure it is clear that the dimensions of the cuboid are 6 cm, 8 cm and 5 cm.
So, the volume of the cuboid is:
[tex]V_1=length\times width\times height[/tex]
[tex]V_1=6\times 8\times 5[/tex]
[tex]V_1=240[/tex]
The volume of the cuboid is 240 cubic cm.
The area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
Thus, the base area of the triangular prism whose base is 8 cm and height 4 cm, is:
[tex]B=\dfrac{1}{2}\times 8\times 4[/tex]
[tex]B=16[/tex]
The volume of a triangular prism is:
[tex]V_2=Bh[/tex]
Where, B is the base area and h is the height of the prism.
The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:
[tex]V_2=16(5)[/tex]
[tex]V_2=80[/tex]
Now, the volume of the given figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=240+80[/tex]
[tex]V=320[/tex]
Hence, the volume of the finished object is 320 cubic cm.
