In this video I determine the volume of a region whose distance is at most 1 from a box. To understand how to solve this, I solve the 2D case first and solve the area around a rectangle. In the 2D case, the region can be divided into 5 rectangles and 4 quarter circles. In the 3D case, the region can be divided into 7 rectangles, 12 quarter cylinders, and 8 one-eighth spheres. Summing all these up we obtain the volume in the 3D case and area in the 2D case.
Timestamps:
- Problem 2: Volume around a box: 0:00
- Solution: Solve the 2D case first: 0:42
- Area around a square is LW + 2L + 2W + pi
- Solving the 3D case: 3:54
- Volume around a box is LWH + 2(LW + LH + WH) + pi(L + W + H) + 4/3 pi: 14:51
Video notes and playlists:
- HIVE notes: https://peakd.com/hive-128780/@mes/jlgigkdl
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_7Jd6ZORHFQMk8jbwmkos
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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