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3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone.

(a) Sketch the roof of the castle tower. Label the known lengths as described and
label the unknown length as x.
(b) What is the slant height of the roof?

Respuesta :

c=hypotenuse=slant  height
a=base=radius= 12 m
b=height=16 m
thus the slant height will be:
c^2=16^2+12^2
c^2=256+144
c^2=400
⇒c=sqrt (400)
c=20

Therefore, thaaa answer is 20 

Hope This Help................ Have A Nice Daaaay! 

The slant height of the roof x is 20 m.

What is cone?

The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

Let consider the dimensions of the given cone;

c = hypotenuse=slant  height

a = base = radius = 12 m

b = height = 16 m

SO,

[tex]x^{2} =12^{2} + 16^{2} \\x^{2} =144 + 256\\ x^{2} =400\\x=20m[/tex]

Hence, The slant height of the roof is 20 m.

Learn more about cone here:

https://brainly.com/question/26093363

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