Use derivative of volume to find weight of a shpere

[rburt]

Suppose a soccer ball is made of leather 1/8 in thick. If the outside diameter is 9 in, and the density of leather is assumed to be 0.64 oz/cubic in. Use the derivative of volume to get a linear approximation to figure the weight of the ball (assume the ball is spherical).
Work already done: dV=4piR^2
I don't know where to go from here.

 

[uart]

Suppose a soccer ball is made of leather 1/8 in thick. If the outside diameter is 9 in, and the density of leather is assumed to be 0.64 oz/cubic in. Use the derivative of volume to get a linear approximation to figure the weight of the ball (assume the ball is spherical).
Work already done: dV=4piR^2
I don't know where to go from here.

You left out an important part of that expression rburt.

dV=4 \pi r^2 \ \mathbf{dr}Can you think of how this expression is hinting to us about how to estimate the volume of a thin shell. (Hint. What is the expression for the surface area?)

 

[rburt]

I understand that the derivative is the surface area but I do not understand how that relates to the weight of the sphere. I also know that the rate at which the volume of a sphere increases when the radius r increases is the measure of the surface area if the sphere but I do not understand what step is next once you have the surface area and how it relates to the weight.

 

[swill777]

I understand that the derivative is the surface area but I do not understand how that relates to the weight of the sphere.

Find out how much material you have, and use the density to find the weight.

 

[rburt]

How would i do it using linear approximation?

 

[LCKurtz]

If you cut the soccer ball so you could lay it out flat, its volume would be its area times its thickness. Of course, it won't actually lay flat, so that's just an approximation. But look at the formula in uart's post #2. That is a linear approximation.