Question

use a pythagoras ruleto find the slant height of a cone which has a height of12cm and a base diameter of10cm

Answer 1

the base radius is 5

draw a side view and you can see that the slant height s is
s^2 = 5^2 + 12^2
s = 13

You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.