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        riddles >> medium >> Volume of Water
        
(Message started by: codpro880 on Jan 23rd, 2009, 10:15am)
Title: Volume of Water
Post by codpro880 on Jan 23rd, 2009, 10:15am
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.
Title: Re: Volume of Water
Post by SMQ on Jan 23rd, 2009, 10:39am
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 [hide]2cm + 3cm + sqrt[(2cm + 3cm)2 - (9cm - 2cm - 3cm)2] = 5cm + sqrt[(5cm)2 - (4cm)2] = 8cm[/hide].  From here the required volume derives by simple geometry as [hide]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[/hide].

--SMQ


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