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
