# Calculus

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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 -

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 -

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 -

Actually, the formula for the volume of a HEMIsphere is (4/6)pi(r)^2

• Calculus -

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.100000 cm thick to a hemispherical dome with a diameter of 55.000 meters.

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