Question

The roof of a turret is shaped like a cone. The base of the cone is 30 m across and the height is 8 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 turret. Label all lengths, using x as the unknown.
(b) What is the slant height of the roof? Answer:

Answer 1

Solution given:

base=diameter [d]=30m

radius [r]=d/2=15m

height [H]=8m

slant height [l]=xm

we have

∆ ABC is a right angled triangle

base[b]=r

perpendicular [p]=H

hypotenuse [h]=x

by using Pythagoras law

h²=p²+b²

x²=H²+r²

x²=8²+15²

x=√289

x=17m

the slant height of the roof is 17m.