Chapter 2.6, Problem 60E

Cost and tolerance. A firm contracts to paint the exterior of a large water tank in the shape of a half-dome (a hemisphere) The radius of the tank is measured to be 100 ft with a tolerance of $\pm 6in\left(\pm 0.5ft\right)$

(The formula for the surface area of a hemisphere is $A=2\pi r^2,$ as an approximation for $\pi$

) Each can of paint costs $30 and covers $300{\text{ft}}^{\text{2}}$

a. Calculate $dA,$ the approximate difference in the surface area due to the tolerance

b. Assuming the painters cannot bring partial cans of paint to the job, how many extra cans should they bring to cover the extra area they may encounter?

c. How much extra should the painters plan to spend on paint to account for the possible extra area?