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What 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=

What is the radius of the filled region of the cone namely CD rounded to the nearest hundredth if neededA cone with a slant height of 16 cm and a radius of 7 cm class=

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calculista

Answer:

[tex]CD=6.51\ cm[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem Triangles ABE and CDE are similar by AA Similarity Theorem

so

[tex]\frac{AE}{CE}=\frac{AB}{CD}[/tex]

step 1

Find the value of AE

Applying the Pythagorean Theorem in the right triangle ABE

[tex]BE^2=AB^2+AE^2[/tex]

[tex]16^2=7^2+AE^2[/tex]

[tex]256=49+AE^2[/tex]

[tex]AE^2=256-49[/tex]

[tex]AE^2=207[/tex]

[tex]AE=\sqrt{207}\ cm[/tex]

step 2

Find the value of CD

[tex]\frac{AE}{CE}=\frac{AB}{CD}[/tex]

substitute the given values

[tex]\frac{\sqrt{207}}{\sqrt{207}-1}=\frac{7}{CD}[/tex]

[tex]CD=(7)\frac{\sqrt{207}-1}{\sqrt{207}}[/tex]

[tex]CD=6.51\ cm[/tex]

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