SOLUTION: Hi, I was wondering if someone could help me with this problem. A right circular cone of height 10m and base radius 5m has density given by p(x) = 100(20 - x) kg/m^3, where x i

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Question 222764: Hi, I was wondering if someone could help me with this problem.
A right circular cone of height 10m and base radius 5m has density given by p(x) = 100(20 - x) kg/m^3, where x is the perpendicular distance from the base. Find the total mass M of the cone.
Thanks, Judy
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A right circular cone of height 10m and base radius 5m has density given by p(x)
= 100(20 - x) kg/m^3, where x is the perpendicular distance from the base.
Find the total mass M of the cone.
:
p(x) = 100(20 - x)
Find the density: x = 10, (the height from the base)
p(x) = 100(20 - 10)
p(x) = 100(10)
p(x) = 1000 kg/cu.meter
:
Find the Volume of a cone: V = %281%2F3%29%2Api%2Ar%5E2%2Ah
V = %281%2F3%29%2Api%2A5%5E2%2A10
V = %281%2F3%29%2Api%2A25%2A10
V = 261.8 cu/meters
then
Mass = 261.8 * 1000
Mass = 26,1800 kg