Use differentials to estimate the amount of material in a closed cylindrical can that is 20 cm high and 8 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximating the volume of metal which makes up the can (i. e. melt the can into a blob and measure its volume), not the volume it encloses

The volume is  

Step-by-step explanation:

From the question we are told that

    The height is  h =  20 cm

    The diameter is  d = 8 cm

    The thickness of both top and bottom is  dh  =  2 * 0.1  =  0.2 m

     The  thickness of one the side is dr =  0.1 cm

The  radius is mathematically represented as

substituting values

Generally the volume of a cylinder is mathematically represented as      

Now the partial differentiation with respect to h is  

Now the partial differentiation with respect to r is  

Now the Total differential of is mathematically represented as

substituting values

i believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}