Question

Use differentials to estimate the amount of metal in a closed cylindrical can that is 22 cm high and 10 cm in diameter if the metal in the top and the bottom is 0.4 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.) cm3

Answer 1

97.43cm³

Explanation:

h = 22cm

d = 10cm

r = d/2

= 10/2

= 5

dh = 2(0.4)

= 0.8

dr = 0.05

V = πr²h

dV = d(πr²h)

Such that

πd(r²h)

= π[(r²dh + hd(r²)]

dV = π[(r²dh + 2rhdr]------(1)

When we put the values above in this equation 1 above:

dV = π[(5)²*0.8 + 2*5*22*0.05]

= π(25*0.8+11)

= π31cm³

Multiply the value of pi with 31cm³

= 97.43cm³