A cone has radius 9 and height 12. A frustum of this cone has height 4.

What are the radii of the bases of the frustum?

The radii of the frustrum bases is 12

Step-by-step explanation:

In the figure attached below, ABC represents the cone cross-section while the BCDE represents frustum cross-section

As given in the figure radius and height of the cone are 9 and 12 respectively

Similarly, the height of the frustum is 4

Hence the height of the complete cone= 4+12= 16 (height of frustum+ height of cone)

We can see that ΔABC is similar to ΔADE

Using the similarity theorem

AC/AE=BC/DE

Substituting the values  

12/16=9/DE

∴ DE= 16*9/12= 12

Hence the radii of the frustum is 12  

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