Question

He 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.

What is the slant height of the roof?

Answer 1

Answer: 20 meters

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Step-by-step explanation:

The base of the cone is 24 m across. This is the diameter of the circle. Divide it in half to get 24/2 = 12 m as the radius.

We can form a right triangle inside the cone such that the horizontal piece is the radius 12 m and the vertical piece is the height 16 m. The hypotenuse of this right triangle is the slant height. This is all mentioned in the instructions of course.

We'll use the pythagorean theorem to find the hypotenuse.

`a^2 + b^2 = c^2\\\\c = √( a^2 + b^2 )\\\\c = √( 12^2 + 16^2 )\\\\c = √( 144 + 256 )\\\\c = √( 400 )\\\\c = 20 \text{ meters is the slant height}\\\\`

It is the distance from the circular base to the peak of the cone, when traveling along the outside of the cone. This is a straight line distance.