posted by Rebekah on .
I am sooo confused on my homework.
#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)
d^2 = (30t)^2 + (40t)^2 = 2500t^2
d = 50 t
(did you notice that the triangle is the 3:4:5 right-angled triangle? )
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)
(1/8)π(4R^2 h - h^3)
check my arithmetic, I should have written it out on paper first.
thanks so much! where di the 3/8 come from??