[tex]\text{Volume of the object = 154 in}^3[/tex]Explanation:
The figure comprise of a cone and a rectangular prism. To find the volume, we will find the volume of the cone and volume of the rectangular prism. Then we will sum the results.
[tex]\text{Volume of a cone = }\frac{1}{3}\times\pi r^{2}h[/tex]
height = 10 in
diameter = 6 in
radius = diameter/2 = 6/2
radius = 3 in
π = 3
[tex]\begin{gathered} \text{Volume of the cone = }\frac{1}{3}\times3\times3^2\times10 \\ \text{Volume of the cone = 9}0in^3 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume of a rectangular prism = length }\times\text{ width }\times\text{ height} \\ V\text{ = lwh} \end{gathered}[/tex]
Length = 8 in
width = 8 in
height = 1 in
[tex]\begin{gathered} \text{Volume of the rectangular prism = 8 }\times\text{ 8 }\times\text{ 1} \\ \text{Volume of the rectangular prism = 64 in}^3 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume of the object = Volume of the cone + volume of the rectagular prism} \\ \text{Volume of the object = 90 + 64} \\ \text{Volume of the object = 154 in}^3 \end{gathered}[/tex]
