# Calc

You plan to paint a sphere of radius 200 cm with a coat of pain .2 cm thick. Use differentials to approximate the amount of paint that is needed. Use the equation for the volume of a sphere.

1. 👍
2. 👎
3. 👁
1. v = 4/3 πr^3
dv = 4πr^2 dr
so, dv = 4π*200^2*.2 = 32000π cm^3

note that the dv is just the surface area times the thickness, as you'd expect for tiny thicknesses.

1. 👍
2. 👎

## Similar Questions

1. ### physics

A mettalic sphere of radius a carries a charge Q. It is brought in contact with an uncharged sphere of radius b . what will be the charge on the first sphere. My work I eliminated 2 options by substitution and realised that it

2. ### Calculus

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.02 cm thick to a sphere with diameter 40 meters. (Recall that the volume of a sphere of radius r is V=(4/3)πr^3. Notice that you are given that

3. ### calculus

3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of

4. ### science

A sphere of radius 4 cm iss carved from a homogenous sphere of radius 8cm and mass 160g. the mass of the smaller sphere is

1. ### math

A painter needs to purchase enough paint to paint a bedroom that consists of four walls. Two of the walls are 11 feet by 10 feet and the other two walls are 12 feet by 10 feet. The paint is sold in 1 gallon cans, and each gallon

2. ### Calculus

Use linear approximation or differentials to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.010000cm thick to a hemispherical dome with a diameter of 75.000meters.

3. ### Geometry

A plane intersects a sphere that has a radius of 13cm. The distance from the center of the sphere to the closest point on the plane is 5 cm. What is the radius of the circle that is the intersection of the sphere and the plane? A.

4. ### Calculus Help

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)

1. ### Physics

Two uniform solid spheres have the same mass of 3 kg, but one has a radius of 0.25 m while the other has a radius of 0.8 m. Each can rotate about an axis through its center. (a) What is the magnitude τ of the torque required to

2. ### Physics

An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of

3. ### Homework Help Calculus

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

4. ### math

A solid cone of height 12cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere. cone V= 1/3 pi r^2 h sphere V= 4/3 pi r^3 area of sphere = 4r^2 how to find sphere of radius?