Two vases

Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter d = 20 cm; the second vase has the shape of a truncated cone with the lower base d1 = 25 cm and with the diameter of the upper base d2 = 15 cm. Which vase can hold more water if the height of both vases is 0.5 m?

Correct answer:

V1 =  5235.9878 cm3
V2 =  5104.1667 cm3

Step-by-step explanation:

d=20 cm d1=25 cm d2=15 cm  h=0.5 m cm=0.5 100  cm=50 cm  r=d/2=20/2=10 cm r1=d1/2=25/2=252=12.5 cm r2=d2/2=15/2=152=7.5 cm  V1=13 π r2 h=13 3.1416 102 50=5235.9878 cm3
S1=π r12=3.1416 12.52490.8739 cm2 S2=π r22=3.1416 7.52176.7146 cm2  V2=13 h (S1+S1 S2+S2)=13 50 (490.8739+490.8739 176.7146+176.7146)=3062565104.1667 cm3  V2<V1  Verifying Solution:   V2=13 h (r12+r1 r2+r22)=13 50 (12.52+12.5 7.5+7.52) cm3=306256 cm3=5104.1667 cm3

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