WEBVTT

1
00:00:00.000 --> 00:00:06.374
Here is the problem: Find the volume and surface area of a square pyramid with base side 10 and height 12.

2
00:00:06.824 --> 00:00:14.463
Compute the volume (cubic units) and total surface area (square units) of the solid from its dimensions in one length unit.

3
00:00:15.263 --> 00:00:18.491
Volume: one third of base area times height.

4
00:00:18.941 --> 00:00:21.762
Slant height of each triangular face.

5
00:00:22.212 --> 00:00:25.579
Surface area: base plus four triangles.

6
00:00:26.379 --> 00:00:33.925
So the answer is Volume equals 400 cubic units; surface area equals 360 square units.

7
00:00:34.376 --> 00:00:45.440
Volume counts unit cubes inside a solid; surface area counts unit squares needed to wrap it. Doubling every length multiplies volume by 8 and surface area by 4.

8
00:00:46.240 --> 00:00:50.629
Volume 400 and surface area 360 are positive.