Question

Find the diameter of the circular base of right circular cone whose slant height is 8cm and semi vertex angle is 60°​

Answer 1

Answer:

Step-by-step explanation: the slant height (l), the height(h), and the radius of the base(r) make a right anglde triangle. So, when we apply pyhagoras theorem

$8^{2}$ = $h^{2}$ +$r^{2}$

Tan 60= $\sqrt{3}$= radius/ height

So, height = r/$\sqrt{3}$

substitute in pythagoras theorem

64= ($r^{2}$/3) + $r^{2}$ = (4/3)$r^{2}$

$r^{2}$ = 64(3/4) = 48

So, r= $\sqrt{48}$ = 4$\sqrt{3}$

Answer 2

semi vertex angle = 60°

diameter = 2xRadius

slant height l = 8cm

sin 60°= √3/2

√3\2 =p\8

(cross multiple) = p=8√3\2

p=4√3

radius= 4√3

diameter=2x4√3

=8√3