Respuesta :

we can see that

upper part is cone

bottom part is cylinder

Volume of cone:

we are given

[tex]r=8in[/tex]

[tex]h=14in[/tex]

now, we can use volume formula

[tex]V=\frac{1}{3} \pi r^2 h[/tex]

now, we can plug values

and we get

[tex]V=\frac{1}{3} \pi (8)^2 (14)[/tex]

[tex]V=\frac{896\pi }{3} [/tex]

Volume of cylinder:

we are given

[tex]r=8in[/tex]

[tex]h=20in[/tex]

now, we can use volume formula

[tex]V= \pi r^2 h[/tex]

now, we can plug values

and we get

[tex]V= \pi (8)^2 (20)[/tex]

[tex]V=1280\pi  [/tex]

now, we can add both volumes

[tex]V=\frac{896\pi }{3}+1280 \pi [/tex]

we get

[tex]V=\frac{4736\pi }{3}in^3 [/tex]..............Answer

carlos2112

Answer:

[tex]V_T= \frac{4736\pi}{3} \approx4959.5\hspace{3}in^3[/tex]

Step-by-step explanation:

The volume of a cone like this is given by:

[tex]V=\frac{1}{3} \pi r^2 h[/tex]

Where:

[tex]r=Base \hspace{3}radius\\h=Height[/tex]

And the volume of a cylinder is given by:

[tex]V=\pi r^2 h[/tex]

Where:

[tex]r=Radius\\h=Height[/tex]

Now, let:

[tex]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[/tex]

The volume of the composite figure will be given by:

[tex]Volume\hspace{3}of\hspace{3}the\hspace{3}composite\hspace{3}figure=V_T=V_1+V_2[/tex]

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

[tex]r_1=r_2=8in[/tex]

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

[tex]V_1=\frac{1}{3} \pi (8)^2(14)=\frac{896 \pi}{3}\hspace{3}in^3[/tex]

And the volume of the cylinder is:

[tex]V_2=\pi (8)^2(20)=1280\pi \hspace{3}in^3[/tex]

Finally, the volume of the composite figure is:

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

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