Search problems

3 problems match “space diagonal”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Product of cube diagonal lengths ●●○○○ 20 ptsA cube has side length 1. Find the product of the lengths of the diagonals of this cube, where a diagonal is a line segment between two vertices that is not an edge.
2. Surface area from edge sum and diagonal ●●○○○ 20 ptsThe sum of the lengths of the twelve edges of a rectangular box is $140$, and the distance from one corner of the box to the farthest corner is $21$. What is the total surface area of the box?
3. Center of a cube from three vertices ●●●○○ 50 ptsThree vertices of a cube in space have coordinates $A = (2,3,0)$, $B = (0,5,4)$, and $C = (4,1,8)$. Find the coordinates $(x, y, z)$ of the center of the cube.