how do i calculate the slant heigth for the given cone if the diameter is 8 and the heigth is 9

Convert n diameter to radius = 8/2 = 4

Then use Pythagorean theorem:

r^2 + h^2 = slant^2

Consider a cross-section, you should see a right-angled triangle

with a base of 4 and a height of 9
h^2 = 4^2 + 9^2
= ...
h = √...