A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the cylindrical shell, in cm, if it has height of 40 cm and radius of 5 cm.

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A: Assume the area to be A and the side length be a. Use the derivative to determine the error dA for a…

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A: Given, The diameter of the circular plate,d=3.5feet The radius of the circular…

Q: A tin can has a circular base of radius 2 inches and height of 6 inches. If the thickness of its…

A: We have to find the volume of tin can using differentials.

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A: This question is taken from the differentiation in which we have to find the relative error in the…

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A: We need to find the material needed to make a container.

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A: Let the side length of the cube be S = 29.Side increase on each side = 0.03 cm.Total increase in…

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

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Q: The height and base radius of a circular cylinder are measured as 15 cm and 4 cm, respectively, with…

A: Note the formula and result . Volume of cylinder is . Suppose f and g is a differentiable function…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: Given : θ = 26.75°

Q: 3. The edge of a cube is measured to be 6 inches with a possible error of ±0.1 inch. Estimate the…

A: The error in measuring the edge of the cube is 0.1 inches. to find the error in the surface area and…

Q: The radius of a spherical balloon is measured to be 9 inches, with a possible error of 0.03 inch.…

A: we know that  surface area of sphere =4pi r^2 where r is the radius of sphere  Given radius of…

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 14 cm high and…

A: *given:- radius of the cylindrical can, R = 6/2 = 3 cm height of the cylindrical can, h = 14 cm

Q: Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick. If…

A: Answer: 40π cm³ or 125.66 cm³

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a…

A: Using differential to estimate the amount of paint needed to apply a coat of paint of 0.05cm thick

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: The solution are next step

Q: The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then…

A: Let the side of the cube = s = 10 cmError in the side = ds = ±0.03 cmNow,Volume of the cube = V =…

Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

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A: The volume of a right circular cone is given as, V=13πr2h The volume of the cone is a function of…

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A: The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. Let…

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and…

A: Given a closed cylindrical can has height 30 cm and 6 cm is diameter. the metal in the top  and…

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A: radius of a circle increases by 3%,

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A:

Q: The length and width of a rectangle are measured as 89 cm and 22 cm, respectively. The error in…

A: According to the given information:Length of rectangle (l) = 89cmWidth of rectangle (b) = 22cmError…

Q: The radius of a sphere is given as 27 cm with a maximum error in measurement of .05 cm. Use…

A: From the given data:Radius of the sphere r=25cmMaximum error in radius of the sphere Δrr=0.05…

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A: Given that a coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of…

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A: We are given that each side of a square is 8±0.1. Let x be the side of square and then the side of…

Q: 2. Assume Barry Bonds's head is a perfect sphere. If Dr. Beeresgood measures Barry's head's radius…

A: Given: r=5.8 in∆r=±0.021 in

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A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: A certain cube with side equal to 5 inches is said to have an incremental error of 0.1 inch in its…

A: Topic :- Application of Derivative  Volume of cube = (side)3

Q: 2. The radius and height of a right-circular cylinder are measured with errors at most 0.1 inches.…

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Q: V9.22

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Q: The inside radius of a pipe is 4.50 cm. By using differentials, find the approximate volume of metal…

A: According the problem, we have

Q: An astronaut using a camera measures the radius of Earth as 4000 mi with an error of ±80 mi. Use…

A: Please see the explanation below

Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 11…

A: Let r and h be radius and height of tin can Then r varies from 4 cm to 4.04 cm and height changes…

Q: A painting contractor charges Php 120 per sq.m. for painting the four walls and ceiling of a room.…

A:

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

A:

Q: The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement…

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Q: The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of…

A: Solution:- It is given that the radius of the end of a log=28 inches. ⇒r=28 inches possible…

Q: A goldsmith is tasked to coat a closed rectangular box with gold 0.1 cm thick. The height of the box…

A:

Q: The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.…

A:

Q: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

A: Here we find the error in volume by using differential.

Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 12 cm and height…

A: The volume of a cylinder is given by the expression . Thus the volume of a thin cylinder is obtained…

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

A:

Q: a machinist is required to manufacture a square metal plate with the side length of 5cm.  if the…

A: The length of the metal plate is x=5cm. The machinist is allowed an error of 0.3 cm. The area of the…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: We need to choose correct option.

Q: the width and length of rectangle are measure in cm as 6 and 18 respectively with an error of at…

A: