Question

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

Answer 1

Answer:

$V_T= \frac{4736\pi}{3} \approx4959.5\hspace{3}in^3$

Step-by-step explanation:

The volume of a cone like this is given by:

$V=\frac{1}{3} \pi r^2 h$

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:

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

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:

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

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

$V=\frac{1}{3} \pi r^2 h$

now, we can plug values

and we get

$V=\frac{1}{3} \pi (8)^2 (14)$

$V=\frac{896\pi }{3}$

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

$V=\frac{896\pi }{3}+1280 \pi$

we get

$V=\frac{4736\pi }{3}in^3$..............Answer