Question

A solid cone of height 12 cm and base radius 6 cm has the top 4 cm removed as shown in the adjoining below. Find the whole surface of the remaining solid.

Answer 1

In triangle ABE and ACD, BE∥CDSo △ABE~△ACDABAC=BECD412=BE6⇒BE=2cmNow AD=AC2+CD2=144+36=13.41Total surface area of complete cone=πrr+l=π×66+13.41=365.8 cm2Now curved surface area of smaller cone of height 4 cm and radius 2 cm=πrll=AB2+BE2=16+4=4.47So curved surface area=π×2×4.47=28.08 cm2Now totalsufrace area of remaining cone or frustum of cone=total surface area of bigger cone-curved surface area of smaller cone+area ofbase of smaller cone=365.8-28.08 +π×22=350.27 cm2