A semicircular sheet of metal of diameter 28 cm is the bent into an open conical cup. Find the depth and the capacity of the cone.
Diameter of the circular sheet is 28 cm.
Radius =14 cm
Circumference of semicircular sheet =14π cm
Now the semicircular sheet is bent into an open circular cup.
Slant height of conical cup =l= radius of circular sheet =14 cm
Circumference of the base of conical cup = Circumference of semicircle sheet = πr=14π (∵R=7 cm)
Depth of conical cup = Height of cone =h=√l2−r2
=√(14)2−(7)2
=√196−49
=√147
=7√3 cm
Capacity of the conical cup =13πR2h
=13×227×72×7√3
=1078√33 cm3