From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
Lateral and surface areas of cones? There's an app for that. And if there isn't an app, there's a formula.
L = πrl
Our radius is 4 cm and our slant height is 5 cm. Plug those bad boys in.
L = π × 4 cm × 5 cm L = 62.8 cm2
That was easy enough. Surface area is just code for "add in the area of the circular base." For cones it is, anyway.
SA = L + πr2 SA = 62.8 cm2 + π × (4 cm)2 SA = 113.1 cm2
We have a soft spot in our hearts when it comes to cones. Well, soft serve, anyway.
Find the surface area of the solid.
This shape is a little weird. Before we calculate anything, we should come up with an overall surface area formula. The total surface area is the lateral area of a cylinder, and the two lateral areas of the cones.
SA = LCylinder + 2LCone
The lateral area of a cylinder is the circumference of the circle times the length of the cylinder. Circumference is two times the radius times our favorite dessert.