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codpro880
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Volume of Water   Untitled1.png
« on: Jan 23rd, 2009, 10:15am »		 Quote Quote Modify Modify
A 9-cm-diameter right circular cylinder contains two spheres with
radii 3 cm and 2 cm as shown below.
Find the volume of liquid needed just to cover the spheres.
 
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Re: Volume of Water  
« Reply #1 on: Jan 23rd, 2009, 10:39am »		 Quote Quote Modify Modify
Consider the vertical plane passing through the centers of both spheres.  In this plane it is straightforward to see that the depth of liquid needed to just cover both spheres is 2cm + 3cm + sqrt[(2cm + 3cm)2 - (9cm - 2cm - 3cm)2] = 5cm + sqrt[(5cm)2 - (4cm)2] = 8cm.  From here the required volume derives by simple geometry as pi*(4.5cm)2*8cm - pi*2cm3*4/3 - pi*3cm3*4/3 = pi*[162cm3 - (32/3)cm3 - 36cm3] = pi*(346/3)cm3 or approximately 362.33cm3.
 
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