Question

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters.

Answer 1

Answer:

dv= 989100cm^3

Explanation:

The volume of a sphere can be calculated using below formula

Volume of a sphere = 4/3 π r^3

Therefore, for a hemisphere, V= 2/3 pi r^3

V=(4/3)πr³

V= 2/3πr³

dV/dr=4πr²

Then we need to pproximate dV/dr with

ΔV/Δr then we have

Volume of hemispherical some is one half of the the volume of a sphere where dr is change in radius, dv is change in volume

dV/dr=2πr²

Take the derivative of V with respect to r then we have

dV=2πr²dr

where

Radius = diameter/2

Our diameter is 30cm then

r=30m/2 = 15cm

Then we convert to cm we have

r= 1500cm

dv= 2×π ×(1500)^2 × 0.07

dv= 989100cm^3

the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters is

989100cm^3