Read the story problem, and then answer the questions that follow.

Gordon works for a graphic design firm and is creating a label for a food truck vendor.The vendor specializes in finger food and wants to sell food in right conical containers so they're easy for people to hold.To complete his label, Gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container.Gordon has been given a model of the container and told that the diameter is 4 inches and the measure of angle BAC in the model is 72.

Part A

Find the slant height of the cone.The slant height is the distance from the apex, or tip, to the base along the cone's lateral surface.Round to the nearest hundredth, if necessary.Show your work

Part B

Find the height of the cone.Round to the nearest hundredth, if necessary.Show your work.

Part C

Imagine two line segments that each represent a slant height of the cone.The segments are on opposite sides of the cone and meet at the apex.Find the angle formed between the line segments, which is also called the aperture.Show your work.

Part D

To complete the container label, Gordon needs to know the lateral surface area of the container.The lateral surface area is found using, where Ris the radius of the container's base, andis the slant height.What is the lateral surface area of the container?Round to the nearest hundredth, if necessary.Show your work.