Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its 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 answer:

h =  10.2195 cm

Step-by-step explanation:

h1=810.2195 cm h2=28.2195 cm  V = 31 π r2 h V3 = 31 π r12 h1  V1 = VV3 V1 = 31 π r2 h31 π r12 h1 V1 = 31 π (r2 h  r12 h1)  r1<r2<r r1:h1 = r:h r1 = r   h1/h r2:(hh2) = r:h r2 = r   (hh2)/h  V2 = 31 π r22 (hh2)  V1 = V2  31 π (r2 h  r12 h1) = 31 π r22 (hh2) (r2 h  r12 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=2ab±D=22±340=22±285 h1,2=1±9.219544 h1=10.219544457 h2=8.219544457  h>0  h=h1=10.2195=10.2195 cm

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