A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of 113 cm3 for each toy and all toys needs to be packed.(Take π=227)
788
Volume of the toy = volume of hemisphere + volume of cone
Height of the cone, h = √(25)2−(7)2 = 24
=23πr3+13πr2h
= 227×(7)2[2×73+8]
= 1950.66cm3
Volume of the box = πr2h = 227×(70)2100 = 1540000cm3
Volume of the toy + packaging volume = 1950.66+113=5862.983
Number of packaged toys that can fit into the box = volume of boxvolume of packaged toy
=1540000(5862.983
≈ 788.