In this section, you will investigate relationships of the scale factor in similar cones. The animation below shows the relationship between the radius, height, and slant height of a cone. In the diagram below, h represents the height of the cone, r represents the radius, and l represents the slant height. Cones A, B, C, D, and E are similar. One of the cones is shown in the diagram. Some of their lengths are given in the table. Complete the drag and drop puzzle to fill in the table. Drag the appropriate number to its correct place in the table. Click the Reset button if you need to reset the interactive. • Do these ratios hold true for all 5 cones?

Interactive popup. Assistance may be required.

• Is more information needed to show that these cones are similar?

Interactive popup. Assistance may be required.

Now, let’s look more closely at the volumes of similar cones. The volumes of three similar cones are shown below. Click on each volume to see how the volume was calculated.

 Volume of Cone A (cubic units) Volume of Cone B (cubic units) Volume of Cone C (cubic units) Interactive popup. Assistance may be required. 16π V = one-third 1 3 πr2h    = one-third 1 3 π(4)2(3)    = one-third 1 3 π(16)(3)    = 16π Interactive popup. Assistance may be required. 128π V = one-third 1 3 πr2h    = one-third 1 3 π(8)2(6)    = one-third 1 3 π(64)(6)    = 128π Interactive popup. Assistance may be required. 432π V = one-third 1 3 πr2h    = one-third 1 3 π(12)2(9)    = one-third 1 3 π(144)(9)    = 432π  Investigate volume relationships by completing the following drag and drop puzzle. Use the information in the volume calculations above to help you. Drag the appropriate tiles to the correct place on the table. Click the Reset button if you need to reset the interactive.

Use the information in the table you just completed to answer the following questions.