Question

The two cones are similar. Find the volume of the larger cone. Round your answer to the nearest hundredth. (picture below)

Answer 1

B~2850.70ft^3

Explanation

Answer 2

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.


`(20)/(12) = (r)/(7) \\\\\sf{Cross~multiply}\\\\7 \cdot 20 = 12r\\\\r = (7\cdot 20)/(12)\\\\ r = (140)/(12) = (70)/(6) = (35)/(3)`

The radius can be simplified to 35/3

Now the formula for the volume of a cone is

`\sf{Volume = (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 = (1)/(3) (3.14)( (35)/(3) )^2(20)\\\\V \approx2849.25926\\\\V \approx 2849.26`

To the nearest hundreth, the volume is 2849.26 ft^3.