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.