Question

Find the side length of a cube which can fit inside a perfect sphere with a diameter of 24cm

Answer 1

Ok, so 24 = length of diagonally opposite corners of cube, because this is the diameter of the circle. Visualise cutting the cube diagonally in half to give 2 pyramids. 24 = the diagonal of the base of them. Now to find the sides, we use Pythag: 24^2 = x^2 + x^2 as all sides of a cube are equal. so x = sqr of 288. Now x is the diagonal of a face of the cube, so to find the edges, we need to use pythag again. let y = the edge of the cube, then 2y^2 = 288. So y^2 = 144, so y = 12. Therefore the edges of the cube are 12 cm each.