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December 21, 2014

December 21, 2014

Posted by **Rebekah** on Tuesday, September 18, 2012 at 8:25pm.

#1 Two cars lave an intersection at the same time. One is headed south at a constant speed of 30mph. the other is heading west at a constant speed of 40mph. Build a model that expresses the distance (d) between thec ars as a funtion of time (t)?

#2 Inscribe a right cylinder of height (h) and radius (r) in a a sphere of fixed radius (R) expressed the volume (V) of the cylinder as a function of (h)

- pre calc -
**Reiny**, Tuesday, September 18, 2012 at 8:55pmd^2 = (30t)^2 + (40t)^2 = 2500t^2

d = 50 t

(did you notice that the triangle is the 3:4:5 right-angled triangle? )

#2

volume(cylinder) = πr^2 h

make a sketch, let the radius of the cylinder be r

the radius of the sphere R, and the height of the cylinder as h

let 2H = h , that is let the distance from the centre of the sphere to the centre of the cylinder base be h.

then r^2 + H^2 = R^2, where R is a constant

r^2 = R^2 - H^2

Volume = πr^2 H = π(R^2 - H^2)h

= π(R^2H - H^3)

but H = h/2

Vol = π(R^2 h/2 - h^3/8)

or

(1/8)π(4R^2 h - h^3)

check my arithmetic, I should have written it out on paper first.

- pre calc -
**Rebekah**, Wednesday, September 19, 2012 at 7:22amthanks so much! where di the 3/8 come from??

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