Question

a wedge is cut out of a cylindrical log of radius 100 mm cutting plane with 40 degree angle of inclination. It is observed that this wedge is similar to a bigger wedge whose y2| is 110mm. Compute the volume of the bigger wedge and solve the radius of the log, where the bigger wedge came from.

V2 = _____ mm^3

r2 = ______mm

Answer 1

Given r1=100mm, y2=110mm; y1=r1tan40=100tan40 mm=83.91mm, the length of the smaller cylinder, y2=r2tan40, r2=y2tan50=110tan50 mm=131.09mm, the length of the larger cylinder.

Volume of larger cylinder=π(r2)²y2=π(y2)³tan²50=5,938,830mm³ approx. and r2=131.09mm approx.

The above is a representation of how the wedge appears to have been cut from the cylinder according to the description in the question. A similar wedge was cut where y2=110mm and r2=y2tan50mm. If the cut had been vertical (effectively creating two congruent wedges joined together) we would have had twice the volume of the wedge=half the volume of the larger cylinder, so the volume of the wedge is a quarter the volume of the larger cylinder=1,484,707mm³ approx.