Volume of the cone

Find the volume of the cone with the base radius r and the height v.
a) r = 6 cm, v = 8 cm
b) r = 0,9 m, v = 2,3 m
c) r = 1,4 dm, v = 30 dm

Result

V1 =  301.593 cm3
V2 =  1.951 m3
V3 =  61.575 dm3

Solution:

r1=6 cm v1=8 cm  V1=13 π r12 v1=13 3.1416 62 8301.5929301.593 cm3r_{1}=6 \ \text{cm} \ \\ v_{1}=8 \ \text{cm} \ \\ \ \\ V_{1}=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{1}^2 \cdot \ v_{1}=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 6^2 \cdot \ 8 \doteq 301.5929 \doteq 301.593 \ \text{cm}^3
r2=0.9 m v2=2.3 m  V2=13 π r22 v2=13 3.1416 0.92 2.31.95091.951 m3r_{2}=0.9 \ \text{m} \ \\ v_{2}=2.3 \ \text{m} \ \\ \ \\ V_{2}=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{2}^2 \cdot \ v_{2}=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 0.9^2 \cdot \ 2.3 \doteq 1.9509 \doteq 1.951 \ \text{m}^3
r3=1.4 dm v3=30 dm  V3=13 π r32 v3=13 3.1416 1.42 3061.575261.575 dm3r_{3}=1.4 \ \text{dm} \ \\ v_{3}=30 \ \text{dm} \ \\ \ \\ V_{3}=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r_{3}^2 \cdot \ v_{3}=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 1.4^2 \cdot \ 30 \doteq 61.5752 \doteq 61.575 \ \text{dm}^3



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