A sherically shaped balloon is being inflated so that the radius, r, is changing at the constant rate of 2in/sec. Assume that the radius is zero at time zero.
a. Find an algebraic model for the radius as a function of t, r(t). r(t)=.....
b. Find an algebraic model for the volume of the balloon in terms of the radius, V(r)=......
It's been a long time since I've done parametrics & I can't remember how to write equations....
2007-04-22 08:11:42 · 5 answers · asked by melissa 1 in Science & Mathematics ➔ Mathematics
edit:
10 pts to who can answer this simple parametric problem CORRECTLY
2007-04-22 08:17:31 · update #1
Well the radius would be the amount of time passed multiplied by the rate at which it is increasing
r(t) = 2t
Since the balloon is spherical it's volume is
V(r) = (4/3)*pi*r^3
And if you need V(t), just substitute r = 2t
V(t) = (4/3)*pi*(2t)^3
V(t) = (32/3) * pi* t^3
2007-04-22 08:17:01 · answer #1 · answered by radne0 5 · 0⤊ 0⤋
It is not a parametric problem
r(t) meanas the radius as a function of t
v(t) meanas the volume as a function of t
So
r(t) = 2t where t is the time in seconds
v(t) = 4/3 pi (r^2)= 4/3 pi *(8t^3)
So v(t) = 32/3 pi t^3
2007-04-22 15:23:32 · answer #2 · answered by a_ebnlhaitham 6 · 0⤊ 0⤋
5
2007-04-22 15:13:21 · answer #3 · answered by Ivan R 2 · 0⤊ 1⤋
dr = 2*dt
r =2t inches as at t=0 r=0
V(r)= 4/3 *pi*r^3 and as a function of time
V(t) =4/3pi(2t)^3= 32/3*pi*t^3
2007-04-22 15:21:43 · answer #4 · answered by santmann2002 7 · 0⤊ 0⤋
a) r(t)=2t
b) V(r)=(4/3)*PI*r^3
r in inches
t in seconds
V in in^3
2007-04-22 15:18:39 · answer #5 · answered by G_U_C 4 · 0⤊ 0⤋