Mathematics: Ahemispherical dome of radius 50 feet is to be given 7 coats of paint, each of which is 1/100 inch thick. use linear approximation to estimate the volume of paint needed for the job. ( hint: approximate the change in the volume of a hemisphere when the radius increases from 50 feet to 50 feet 7/100 inches. don t forget to make sure this increased radius is in terms of feet. ) it will take approximately cubic feet of paint to apply all 7 coats of pain.

The answer is Line L is the perpendicular bisector of CCL...

Ahemispherical dome of radius 50 feet is to be given

david6835

06.01.2022

91.67 ft^3

Step-by-step explanation:

We are given that radius of hemispherical dome=50 feet

Number of coats of paint=7

Thickness of each coat of paint= $\frac{1}{100} in$

We have to find the volume of paint by using linear approximation

Volume of hemisphere= $\frac{2}{3}\pi r^3$

Differentiate w.r.t r

Then, we get $\frac{dv}{dr}=2\pi r^2$

$\delta r=\frac{1}{100\times 12}\times 7=\frac{7}{1200} feet$

By approximation

$\delta V=\frac{dV}{dr}\delta r$

Substitute the values then we get

$\delta V=2\pi r^2\cdot \frac{7}{1200}$

$\delta V=2\times \frac{22}{7}\times (50)^2\times \frac{7}{1200}=91.67 ft^3$

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