Question

Two congruent solids S1 and S2 have the property that S1∩S2 is a right triangular prism with height 3 and a base that is an equilateral triangle of side length 2. If the volume of S1∪S2 is 25 units3, find the volume of S1.

Answer 1

S1=9.905 cubic units

Explanation:

As the two solids are congruent it can be said that they have the same angles and the same lengths then their volume is equal and therefore S1= S2 then S1∪S2= S1+S2- S1∩S2 = S1+S1- S1∩S2 =2S1- S1∩S2 =25.

Now, S1∩ S2= Prism volume= (Area of triangle (A)*Height(h)), the area of the equilateral triangle that is the base of the prism is given by A=√3/4*(length Lateral) ^2= A=√3/4*(2^2 )=√3 square units .

Then S1∩ S2=A*h =√3*3=5. 19 cubic units .

Finally you have

2S1- S1∩S2 =25

2S1-5. 19=25 clearing s1 you have

S1=(25-5. 19)/2 = 9. 905 cubic units