Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 1/100cm thick to a hemispherical dome with a radius of 18 meters.

I tried it but I keep getting the wrong answer.Here's what I did below:

sphere:
V = ⁴/₃πr³
A = 4πr²

radius = 18m
0.01cm = 0.0001m
A = 4π(18)² 4071.504079= m²
Volume = 4071.504079m² x 0.0001m = .40715m³ or 40715cm³

Problem of units conversion.

0.4071504079 m³
=0.4071504079×10^6 cm³
=407150 cm³ approximately.

I tried that answer and it still was incorrect

To estimate the amount of paint needed to apply a coat of paint 1/100cm thick to the hemispherical dome, you can use the linear approximation.

First, let's find the surface area of the hemisphere:

A = 2πr²

Given the radius of the sphere is 18 meters:

A = 2π(18)²
A = 2π(324)
A = 648π square meters

Since we want the thickness in centimeters, we convert the thickness of 1/100cm to meters:

0.01 cm = 0.0001 m

Next, we need to find the volume of the paint needed.

Volume = Surface Area x Thickness

Volume = 648π x 0.0001
Volume ≈ 0.0648π cubic meters

To convert the volume to cubic centimeters, we can multiply by 1,000,000:

Volume (in cm³) ≈ 0.0648π x 1,000,000
Volume (in cm³) ≈ 64,800π cubic centimeters

So, the estimated amount of paint needed to apply a coat of paint 1/100cm thick to the hemispherical dome with a radius of 18 meters is approximately 64,800π cubic centimeters.

To estimate the amount of paint needed to apply a coat 1/100cm thick to a hemispherical dome, you can use a linear approximation. Here's how you can do it correctly:

1. Find the surface area of the hemisphere:
The formula for the surface area of a hemisphere is A = 2πr², where r is the radius. In this case, the radius is 18 meters, so A = 2π(18)² = 2π(324) = 648π square meters.

2. Convert the thickness of the paint into meters:
Given that 1 centimeter is equal to 0.01 meters, divide the thickness of the paint by 100:
0.01cm / 100 = 0.0001 meters.

3. Calculate the volume of paint needed:
Multiply the surface area of the hemisphere by the thickness of the paint:
Volume = 648π * 0.0001 = 0.0648π cubic meters.

4. Convert the volume to cubic centimeters:
To convert from cubic meters to cubic centimeters, multiply by 1,000,000:
0.0648π * 1,000,000 = 64800π cubic centimeters, which is approximately 203,646.96 cubic centimeters.

Therefore, the correct estimate for the amount of paint needed to apply a coat 1/100cm thick to the hemispherical dome with a radius of 18 meters is approximately 203,646.96 cubic centimeters.