# Calc help!

1. Sep 25, 2004

### BrendanM

Im very rusty heres my problem, please help thanks!

The radius of a sphere is expanding at the rate of 1 meter/min. At t=0 the radius is 1. In earch case, find the requested function and sketch the curve.

a)The surface area of the sphere as a function of the time;
For this i took: dR/dt = 1 m/min
A=4*Pi*r^2
dA/dt=8*pi*r*dR/dt
dA/dt = 8*pi*r <--- if this is right how do i sketch this graph as a function of time??
my graph points that i ploted were (0,8pi),(1,16pi),(2,24pi) etc... but this is confusing me because at t=0 radius is 1... is my x-axis supposed to be time or radius someone help me im confused..

2. Sep 25, 2004

### phoenixthoth

You are plotting the rate of change of area, not area. So based of the graph of the derivative of area, reconstruct what the graph of area looks like knowing that what you have are slopes. Start at (0,1) and draw a tangent line with slope 8pi. Then at (1,???) where ??? > 1, the tangent line will have slope 16pi. Or if you've done integration, integrate dA/dt and to solve for the "C", plug in the value (0,1). I think your area is parabolic.

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