Answer: [tex]8.66in^3[/tex]
Step-by-step explanation:
The oy rocket shown is formed by a rectangular prism and a regular pyramid whose base is a square.
The volume of the rectangular prism can be calculated with:
[tex]V_{rp}=l*w*h[/tex]
Where "l" is the length, "w" is the width and "h" is the height.
You can observe that:
[tex]l=8in\\w=1in\\h=1in[/tex]
Then, you can substitute values:
[tex]V_{rp}=(8in)(1in)(1in)=8in^3[/tex]
The volume of the regular square pyramid can be calculated with:
[tex]V_p=\frac{s^2*h}{3}[/tex]
Where "s" is the lenght of a side of the base and "h" is the height of the pyramid.
You can observe in the figure that:
[tex]s=1in\\h=2in[/tex]
Substitute into the formula. Then:
[tex]V_p=\frac{(1in)^2(2in)}{3}=\frac{2}{3}in^3[/tex]
The volume of the toy rocket is the sum of the volume of the rectangular prism and the volume of the regular square pyramid. Then:
[tex]V_{toy}=8in^3+\frac{2}{3}in^3=8.66in^3[/tex]
