Use Differentials to Estimate the Amount of Metal in a Closed

Multiple Choice

Use differentials to estimate the amount of metal in a closed cylindrical can that is $12 \mathrm {~cm}$ high and 8 $\mathrm { cm }$ in diameter if the metal in the top and bottom is $0.09 \mathrm {~cm}$ thick and the metal in the sides is $0.01$ $\mathrm { cm }$ thick. (rounded to the nearest hundredth.)

A) $8.34 \mathrm {~cm} ^ { 3 }$
B) $\quad 6.99 \mathrm {~cm} ^ { 3 }$
C) $6.91 \mathrm {~cm} ^ { 3 }$
D) $6.7 \mathrm {~cm} ^ { 3 }$
E) $12.06 \mathrm {~cm} ^ { 3 }$