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The graph shows the relationship between the radius and volume for many cones whose height is 6 inches. 9 DY volume in cubic inches B radius in inches Select all the true statements about such cones. If the radius of the cone doubles, the volume of the cone doubles. The relationship between radius and volume is not linear. The relationship between radius and volume is linear. If the radius of the cone is 2 inches, the volume of the cone is about 25 cubic inches. If the radius of the cone doubles, the volume of the cone is multiplied by 4.

User Piegames
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1 Answer

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Let's evaluate each statement:

1. If the radius of the cone doubles, the volume of the cone doubles:

We can select 2 points; with the second point having twice the radius of the first one. Let's select the points of the graph where radius is 1, and where its radius is twice that: 2. The volume for a cone of radius 1 is about 5, while for twice the radius, 2, the volume is 25. The volume of the cone went from 5 to 25. If it whould have been doubled, the volume of point to would be about 10 instead of 25. Then, statement 1 is false.

2. The relationship between radius and volume is not linear. This is clearly true, since we can see that the graph does not represent a line.

3. The relationship between radius is linear. This statement is false following the same logic of the analysis of the previous statement.

4. If the radius of the cone is 2 inches, the volume of the cone is about 25 cubic inches. This statement is true. The graph show that the corresponding volume to a raidus of 2 is 25.

5. If the radius of the cone doubles, the volume of the cone is multiplied by 4. We can analyze this statement the same way we analyzed the first one. We can selet points of the graph where the radius of the first one is half the radius of the second: when the radius is 1, the volume is 5; when the radius is doubled (2) the volume is 25. We can see that the volume was multiplied by 5 instead of 4 (5x5 = 25). Hence, the last statement is false.

User Dannio
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