Question

PLEASE ASAP ASAPWhat is the radius of the filled region of the cone, namely CD, rounded to the nearest hundredth if needed.

A cone with a slant height of 16 cm, and a radius of 7 cm.


CD=

Answer 1

CD = 6.52 cm

Explanation:

It is given that the cone is right angled cone with, a slant height of 16 cm, and a radius of 7 cm.

By, pythagoras theorm,

`BE^(2) = AE^(2) + AB^(2)`

`16^(2) = AE^(2) + 7^(2)`

`AE^(2)= 256-49 = 207`

`AE = √(207)= 14.387 cm`

Thus, EC = 14.387 - 1 = 13.387 cm,

It can be seen that triangles ABE and CDE are similar.

Thus,

`(AE)/(EC) = (7)/(CD)`

`(14.387)/(13.387) = (7)/(CD)`

CD = 6.513 cm ≈ 6.52 cm