Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Video Summary

The problem involves a cube with a side length of two, where identical hemispherical holes are carved into each face. These holes touch their neighboring holes only at a single point. To find the diameter of each hemisphere, we solve using a right triangle formed by connecting the centers of the cube’s faces and measure diagonally. Both sides of the triangle are one, resulting in the equation \(1^2 + 1^2 = c^2\), where \(c\) is the hypotenuse, equivalent to the hemisphere's diameter. Solving, \(c = \sqrt{2}\). Hence, the diameter of each hole is \(\sqrt{2}\).

Keywords

cube

hemispherical holes

diameter

right triangle

geometry