Question

Find the volume of this object.Use 3 forTr²h3Volume of a Cone=V=TTISinVolume of aRectangular PrismV = lwh9inbin1in[/9inVa[?]in3

Answer 1

`153in^3`

Step-by-step explanation

The volume of the object is the sum of the volumes of the cone and the prism.

The diameter of the cone is given as 6 inches and its height is 8 inches. The radius of a cone is equal to half its diameter, hence, its radius is:

`\begin{gathered} r=(D)/(2)=(6)/(2) \\ r=3in \end{gathered}`

Therefore, the volume of the cone is:

`\begin{gathered} V=(\pi r^2h)/(3) \\ \Rightarrow V=(3\cdot3^2\cdot8)/(3) \\ V=72in^3 \end{gathered}`

The volume of the rectangular prism is:

`\begin{gathered} V=l\cdot w\cdot h \\ \Rightarrow V=9\cdot1\cdot9 \\ V=81in^3 \end{gathered}`

Hence, the volume of the object is:

`\begin{gathered} V=72+81 \\ V=153in^3 \end{gathered}`