82 EXAMPLES. 



depth will the cone sink when it floats with its vertex down- 

 wards ? /* 8/ 



Ans. ^vl8. 



12. A hemispherical vessel, whose weight is w, floats upon 

 a fluid with of its radius below the surface. What weight 

 must be put into the vessel so that it may float with of its 

 radius below the surface? Ans. $//,. 



13. Let the pontoon in Ex. 4, Art 26, be a cylinder, 

 length I, with hemispherical ends, radius r ; to find the 

 load requisite to sink the pontoon to a given depth a. 



Ans. [Al + no 2 (r $a)] 62.5, 

 where A = the area ADK (Fig. 22). 



14. Required the thickness of a hollow globe of copper 

 whose density is 9 times that of water, so that it may just 

 float when wholly immersed in water, r being the exterior 

 radius. Ans. r(l f-v/3). 



15. A cubical box, the volume of which is one cubic foot, 

 is three-fourths filled with water, and a leaden ball, the 

 volume of which is 72 cubic inches, is lowered into the 

 water by a string. It is required to find the increase of 

 pressure (1) on the base and (2) on a side of the box. 



Ans. (1) 41f 02.; (2) 32+ oz. 



16. If the height of the parallelepiped in Ex. 2, Art. 28, 

 is 0.9 of the breadth, and if p = |, find the inclination 6 

 that the parallelepiped may float in indifferent equilibrium. 



Ans. 6 = 33 15'. 



17,. What is the weight of a cube of gold whose side is 

 3 ins., its specific gravity being 19.35 ? Ans. 18.89G Ibs. 



18. What is the volume of a piece of platinum whose 

 weight is 10 Ibs., its specific gravity being 22.06 ? 



Ans. 12.533 cu. ins. 



19. A piece of lead, whose weight is 511.65 grs., weighs 

 in water 466.57 grs. Required its specific gravity. 



Ans. 11.35. 



