First we need to find the radius of the larger cone before we proceed to solve for the volume.
Since they are similar figures, we can set up a proportion and solve for the radius of the larger cone.
\(\frac{20}{12} = \frac{r}{7} \\\\\sf{Cross~multiply}\\\\7 \cdot 20 = 12r\\\\r = \frac{7\cdot 20}{12}\\\\ r = \frac{140}{12} = \frac{70}{6} = \frac{35}{3}\)
The radius can be simplified to 35/3
Now the formula for the volume of a cone is
\(\sf{Volume = \frac{1}{3}\pi r^2h\)
Plug in what we know and what we were given and solve for volume. Also use 3.14 for pi. When questions ask for a decimal approximation they want you to use 3.14 for pi. That's something I've observed after answering thousands of questions :P
\(V = \frac{1}{3} (3.14)( \frac{35}{3} )^2(20)\\\\V \approx2849.25926\\\\V \approx 2849.26\)
To the nearest hundreth, the volume is 2849.26 ft^3.
