- #1

mlschiff

- 4

- 0

## Homework Statement

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 54 m. (Round the answer to two decimal places.)

## Homework Equations

V = 1/2(4/3(pi*r^3)) = 1/2(4/3(pi*(1/2D)^3)) = 1/2(4/3*pi(1/8D^3)) = 1/12pi*D^3

## The Attempt at a Solution

How does V change if we change d from 54m to (54 = 0.03*10^-2)m?

dV/dD = 1/4*pi*D^2

dV = 1/4*pi*D^2*dD

= 1/4*pi*(54)^2(0.03*10^-2)

I got 0.679 as an awesome and got it wrong...