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.
surface of a sphere ... 4 π r^2
approx 9000 m^2
10000 cm^2 in a m^2
use half that area, hemisphere
oops ... missed the hemi
To estimate the amount of paint needed to apply a coat of paint to a hemispherical dome, we can use linear approximation.
First, let's calculate the surface area of the hemispherical dome. The formula for the surface area of a hemisphere is given by:
A = 2πr^2
where A is the surface area and r is the radius. In this case, the diameter is given as 55.000 meters, so the radius is half of the diameter:
r = d/2 = 55.000/2 = 27.500 meters
Now we can calculate the surface area:
A = 2π(27.500)^2
Next, we need to find the amount of paint needed to cover an area of 1 square centimeter. Since the thickness of the paint coat is given as 0.100000 cm, the volume of paint required to apply a coat of paint to 1 square centimeter can be calculated as:
V = A * thickness
In this case, V = A * 0.100000 cm
Now we have the volume of paint needed for one square centimeter. To estimate the total amount of paint needed, we need to multiply this volume by the total surface area of the dome.
Total volume of paint needed = A * 0.100000 cm * total surface area
To convert the volume from centimeters to cubic centimeters, we multiply by 1 cm^3/1 cm. Therefore, the final formula for estimating the amount of paint needed to apply a coat of paint to a hemispherical dome is:
Total volume of paint needed = A * 0.100000 cm * total surface area * 1 cm^3/1 cm
You can plug in the values and calculate the result using a calculator.
I assume you are in calculus.
Surface area=4PIr^2=4*PI*5500 cm^2
volume= surface area*.1 cm^3