00:01
Hello, so here we are using the sphere of the form, x minus h, quantity squared, plus y minus k, quantity squared, plus z minus l, quantity squared is equal to r squared.
00:18
So for a, we have the cube with the center at negative 2, 1, 3.
00:23
Side length of 1, so the inscribed square radius equals half the side, which would be one half.
00:30
So therefore, our answer is going to be x plus two squared plus the quantity y minus one squared plus the quantity z minus three squared is equal to one half squared, so it's equal to one -fourth.
00:47
And then for b, the circumscribed square radius equals half the cube diagonal.
00:54
So the cube diagonal is the square root of one squared plus one, square plus one squared.
01:01
That's the square root of three, and the radius then is going to be the square root of three over two.
01:07
So therefore, our answer is going to be x plus two squared plus the quantity y minus one squared plus the quantity z minus three squared is equal to square root of three over two squared is going to be three over four.
01:27
Three over four.
01:29
And then for part c, the plane gives the cube ranges, x going from 2 to 6, y from 5 to 9, and z from 0 to 4...