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anonymous
 4 years ago
grain silos can be described as a hemisphere sitting atop a cylinder. The interior volume V of the silo can be modeled by V=2/3πr^3+πr^2h, where h is the height of a cylinder with radius r. For a cylinder 6m tall, what radius would give the silo a volume that is numerically equal to 24π times the radius?
anonymous
 4 years ago
grain silos can be described as a hemisphere sitting atop a cylinder. The interior volume V of the silo can be modeled by V=2/3πr^3+πr^2h, where h is the height of a cylinder with radius r. For a cylinder 6m tall, what radius would give the silo a volume that is numerically equal to 24π times the radius?

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campbell_st
 4 years ago
Best ResponseYou've already chosen the best response.1this is always fun... \[24\pi r = 2/3 \pi r^3 + \pi r^2 \times6\] divide by pi Simplifying \[24 r = 2/3 r^3 + 6r^2\] \[36r = r^3 + 9r^2\] divide by r \[r^2 + 9r  36 = 0\] solve the quadratic... and remember only the the positive r as length can only be positive

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327395622906:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327395734101:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac12*\frac43*\pi*r^3+\pi*r^2*h=24*\pi*2*r\]
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