Question

Please help. 20 points. Show all work. Thank you.

Answer 1

The lateral area of a cone is the surface area (aka area of the sides of the object) minus the area of the base of the cone.

The equation for the lateral area of a cone is:  $lateral \: area = \pi rl$
where r = radius and l = slant height.

Since you know that the lateral area = $500 \pi \: cm^{2}$ and the radius, r = 50 cm, you can plug those values into the equation for the lateral area and solve for l, the slant height:
$lateral \: area = \pi rl\\ 500 \pi = \pi (50)(l)\\ 500 = 50l\\ l = 10$

The slant height of the cone is A) 10cm.