Question

Find the volume of the composite figure. The cone is a square cone

Answer 1

`V_T= (4736\pi)/(3) \approx4959.5\hspace{3}in^3`

Explanation:

The volume of a cone like this is given by:

`V=(1)/(3) \pi r^2 h`

Where:

`r=Base \hspace{3}radius\\h=Height`

And the volume of a cylinder is given by:

`V=\pi r^2 h`

Where:

`r=Radius\\h=Height`

Now, let:

`V_1=Volume\hspace{3} of\hspace{3} the \hspace{3}cone\\V_2=Volume\hspace{3} of\hspace{3} the \hspace{3}cylinder\\r_1=Radius\hspace{3} of\hspace{3} the \hspace{3}cone\\r_2=Radius\hspace{3} of\hspace{3} the \hspace{3}cylinder\\h_1=Height\hspace{3} of\hspace{3} the \hspace{3}cone=14in\\h_2=Height\hspace{3} of\hspace{3} the \hspace{3}cylinder=20in`

The volume of the composite figure will be given by:

`Volume\hspace{3}of\hspace{3}the\hspace{3}composite\hspace{3}figure=V_T=V_1+V_2`

Since the cone and the cylinder in the composite figure share the same radius:

`r_1=r_2=8in`

Now, using the data provided, the volume of the cone is:

`V_1=(1)/(3) \pi (8)^2(14)=(896 \pi)/(3)\hspace{3}in^3`

And the volume of the cylinder is:

`V_2=\pi (8)^2(20)=1280\pi \hspace{3}in^3`

Finally, the volume of the composite figure is:

`V_T= ((896\pi)/(3) )+(1280\pi)=(4736\pi)/(3) \approx4959.5\hspace{3}in^3`

Answer 2

we can see that

upper part is cone

bottom part is cylinder

Volume of cone:

we are given

`r=8in`

`h=14in`

now, we can use volume formula

`V=(1)/(3) \pi r^2 h`

now, we can plug values

and we get

`V=(1)/(3) \pi (8)^2 (14)`

`V=(896\pi )/(3)`

Volume of cylinder:

we are given

`r=8in`

`h=20in`

now, we can use volume formula

`V= \pi r^2 h`

now, we can plug values

and we get

`V= \pi (8)^2 (20)`

`V=1280\pi`

now, we can add both volumes

`V=(896\pi )/(3)+1280 \pi`

we get

`V=(4736\pi )/(3)in^3`..............Answer