The figure above depicts an agar cube with a side length of 12mm. In an experiment, students submerged the cube in orange dye for 12 hours. The orange dye permeated 1.5mm on each side, as indicated by the shading in the figure. Calculate the volume of the agar cube that remained unpenetrated by the orange dye.

The volume of the agar cube remaining is 729 cubic mm

Step-by-step explanation:

Side of the agar cube= 12mm

Side of the agar cube after penetration= 12-1.5-1.5

= 9mm

The orange dye penetrated 1.5mm each side so the side of the agar cube is 9 mm

Volume = a x a x a

= 9 x 9 x 9

= 729 cubic mm

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)