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?

(a) Allow me to guide you on this one. Sketch a cone shape. At the circular base of the cone, sketch a straight line across through the middle which will be your diameter (most preferably where the slant height meet the circular base). Label it 24 m. From the apex of the cone, drop a straight line which is perpendicular to the diameter meeting it in the middle. Label that line 16 m. Label the line slanting from the top to the bottom x.

(b) The slant height of the roof is 20 m.

x^{2} = 12^{2} + 16^{2} = 144 + 256

x^{2} = 400

x=√400

x=20m