In the diagram the sphere touches each face of the cube at one point-the center of each face. if each side of the cube is 7cm, what is a reasonable estimate for the unoccupied volume of the cube? a: 120cm3
b: 140cm3
c: 160cm3
d: 180cm3

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

7/2

(decimal: 3.5)

welcome ; )

step-by-step explanation: