Suppose cone a and cone b are similar solids with a ratio of 2: 1 between the cones’ slant heights. determine the ratio of the cones’ volumes.

2: 1
4: 1
6: 1
8: 1

8:1.

I actually came looking for the answer myself, and decided to show how to determine it is in fact an 8:1 ratio.

Step-by-step explanation:

The wording is actually really important. Notice the phrase, "similar solids"? This is exactly the key piece of information needed. We can also see that:

- Cones have a 2:1 Ratio (a:b)

- We must find the ratio of the volumes compared to slant height.

Let's set up two sample cones using the provided ratio 2:1. (A:B)

     - Cone B: Radius of 4, height of 12

     - Cone A: Radius of 2, height of 6.

We can find the length of the slant height using the pythagorean theorem since the height, radius, and slant height make a right triangle. (See image attached.)

*Pythagorean theorem =

A and B are the legs of the triangle, the radius and height. The slant height is c, the hypotenuse.

Cone A:

Cone B:

Ok cool, we got the slant heights now.  By looking at that we can confirm there is a 2:1 ratio happening here. Now, we want to solve for volume.

The equation for volume of a cone is:   where r = radius and h = height. Let's use 3.14 as pi.

Cone A:

Cone B:  

Divide 200.96 by 25.12.  You get 8! That means the ratio compared to volume is 8:1.

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Have a great day!

        - Astro

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step-by-step explanation:

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step-by-step explanation: