Question

Put the cones in order from greatest volume (put at the top of the list) to least volume (put at the bottom of the list).

Try to put them in order thinking about the formula instead of actually solving for the volume.

(5 points)
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Answer 1

I don't see the cone sizes in your message. To order them without calculating each volume, use the volume formula

V = (1/3) π r^2 h,

so for comparison you can ignore the common factor (1/3)π and just compare the quantity r^2 · h for each cone.

Tips for quick comparisons
- If heights are equal, the bigger r^2 wins, so larger radius → larger volume.
- If radii are equal, compare heights.
- If one cone is a scaled copy of another by linear factor k, its volume scales by k^3.
- If diameters are given instead of radii, replace r with (d/2) so r^2 = d^2/4 — you can compare using d^2·h (constant factor 1/4 cancels across cones).
- If only slant heights or angles are given, use similar-triangle relations to express r and h and then compute r^2·h.

Send the dimensions (radius/diameter and height for each cone, or the picture) and I’ll order them for you using this method.