Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?

Correct result:

h =  10.2195 cm

Solution:

h1=810.2195 cm h2=28.2195 cm  V=13πr2 h V3=13πr12 h1  V1=VV3 V1=13πr2 h13πr12 h1 V1=13π(r2 hr12 h1)  r1<r2<r r1:h1=r:h r1=r h1/h r2:(hh2)=r:h r2=r (hh2)/h  V2=13πr22(hh2)  V1=V2  13π(r2 hr12 h1)=13πr22(hh2) (r2 hr12 h1)=r22(hh2) (r2 h(r h1/h)2 h1)=(r(hh2)/h)2(hh2)  (h(h1/h)2 h1)=((hh2)/h)2(hh2)  (h(8/h)2 8)=((h2)/h)2(h2) h(h2)=84  h22h84=0  a=1;b=2;c=84 D=b24ac=2241(84)=340 D>0  h1,2=b±D2a=2±3402=2±2852 h1,2=1±9.21954445729 h1=10.2195444573 h2=8.21954445729   Factored form of the equation:  (h10.2195444573)(h+8.21954445729)=0  h>0  h=h1=10.2195=10.2195 cm

Our quadratic equation calculator calculates it.




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