Use differentials to estimate the amount of tin in a closed tin can with diameter 3 inch and height 4 inch, if the top and bottom are 0.02 inch thick and the side is 0.015 inch thick.

dv = 1.03 inch^3

Explanation:

given data:

diameter = 3 inch

radius = 1.5 inch

height 4 inch

top and bottom thickness is 0.02 inch

side thickness = 0.015 inch

we know that volume of the cylinder is given as

by definition of differential we have

where dh = -(0.02  + 0.02) = 0.04 inch    [ sum of top and bottom thickness]

the radius is decreased by 0.02 inch, dr = 0.02 inc,

dv = 37.69*(0.02) + 7.06*(0.04)

dv = 1.03 inch^3

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.