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?

1. campbell_st

this 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

2. anonymous

|dw:1327395622906:dw|

3. anonymous

|dw:1327395734101:dw|

4. anonymous

r=3

5. anonymous

$\frac12*\frac43*\pi*r^3+\pi*r^2*h=24*\pi*2*r$

6. anonymous

thank you very much!