Given:
A figure that contains a right triangular prism and cuboid.
To find:
The volume of the figure.
Solution:
The dimensions of cuboid are 16 in, 7 in and 3 in.
So, the volume of the cuboid is:
[tex]V_1=Length\times Width \times height[/tex]
[tex]V_1=16\times 7 \times 3[/tex]
[tex]V_1=336[/tex]
The base of the prism is a right angle with base 3 in and height 5 in, and the length of the prism is 6 in. So, the base are of the prism is
[tex]B=\dfrac{1}{2}\times Base\times Height[/tex]
[tex]B=\dfrac{1}{2}\times 3\times 5[/tex]
[tex]B=7.5[/tex]
The volume of a prism is:
[tex]V_2=Bh[/tex]
Where, B is the base area and h is the height of the prism.
[tex]V_2=(7.5)(6)[/tex]
[tex]V_2=45[/tex]
The volume of combined figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=336+45[/tex]
[tex]V=381[/tex]
Therefore, the volume of the figure is 381 cubic in.
