There exists a cube that has a center point C. The distance from point C to any of the eight corners of the cube is 7 units.

Question

There exists a cube that has a center point C. The distance from point C to any of the eight corners of the cub is 7 units. Find the volume of the cube to the nearest whole number.

 

It seems like you could break the cube into six pyramids, each with a slant height of 7. Or that there is a right triangle which slices across the cube from opposite points with a hypotenuse of 14. But not sure what to do with either of those bits of info. 

Answer 1

draw the cube

draw a diagonal from the bottom left vertex to the top right vertex

this segment is 14 units

draw the diagonal of the bottom square of the cube

the diagonal of 14 units, the diagonal of the bottom square, and the back vertical edge makes a right triangle

call the base diagonal d and call the edge x

find d first

d and the two equal edges of the square base form a right isosceles triangle

d²=x²+x²

d²=2x²

d=(√2)x

now find the edge, x

14²=d²+x²

14²=[(√2)x]²+x²

196=2x²+x²

196=3x²

x²=196/3

x²=65.333...

x=√65.333

x=8.0829

V=x³

V=(8.0829)(8.0829)(8.0829)

V=528.08231

V=528 cubic units