A spherical ball of wax with a radius of 5 inches is melted and poured into a container shaped like a rectangular prism with a 12 inch x 10 inch base. What is the height of the melted wax in the new shape?

4.36 in

Step-by-step explanation:

To solve this problem we first find the volume of the sphere using the volume formula, after this we set this volume equal to the volume container which is a rectangular prism. After this we simple solve for the height by dividing the volume of the sphere by 12*10 to get the height

So the steps should look like

(4/3)*π*5³=523.599 in³

523.599 in³=12*10*Height

(523.599/(12*10))=4.36 in

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4