Use function to predict volume of prism

Question

I’m trying to figure out how much the length of the base will be at 8 inches for this problem,

the chart is split in two and at the top of the left it is labeled “length of base,x(inches)” and has the numbers 0,1,2,3,4,5 underneath. And on the right side of the chart it is labeled “Volume, v(x)(Cubic inches) and underneath has the numbers 0,1.5,12,40.5,96,and 187.5. Use the function to predict the volume of the prism when the length of the base is 8 inches.

Answer 1

The length of the base will be 8 inches when it is 8 inches. You are asking about the volume.

If you divide the volumes by 1.5, the volume at 1 inches, you will notice a pattern:

1, 8, 27, 64, 125,...

Clearly, V = 1.5 l³

When l = 8, V = 1.5 l³ = 1.5 * 8³ = 1.5 * 512 = 768

The volume of similar shapes is proportional to the cube of a linear measure of the figure (for a polyhedron, the length of a side, for a sphere, the radius, diameter, or circumference, ...

Answer 2

This relation, like the one with the stacking of balls, is cubic. Use my solution as a model.