Posted by **Tenylob** on Tuesday, October 18, 2011 at 10:56pm.

Use linear approximation or differentials to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.010000cm thick to a hemispherical dome with a diameter of 75.000meters.

- Calculus -
**MathMate**, Wednesday, October 19, 2011 at 6:22am
V=(4/3)πr³

dV/dr=4πr²

Approximate dV/dr with

ΔV/Δr, we get

ΔV=4πr²Δr

where

r=75.000/2, and

Δr=0.0001m after conversion to metres.

- Calculus - correction -
**MathMate**, Wednesday, October 19, 2011 at 6:25am
Here's the same answer in the correct units (cubic centimetres).

V=(4/3)πr³

dV/dr=4πr²

Approximate dV/dr with

ΔV/Δr, we get

ΔV=4πr²Δr (in cubic cm)

where

r=75.000/2*100 cm

=3750 cm, after conversion to cm

Δr=0.01cm

- Calculus -
**Anonymous**, Friday, November 8, 2013 at 1:16am
Actually, the formula for the volume of a HEMIsphere is (4/6)pi(r)^2

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