A goldsmith is tasked to coat a closed rectangular box with gold 0.1 cm thick. The height of the box is 5 cm and the sides of its square base are 4 cm long. Use differentials to approximate the volume of gold he needs.

Q: A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21…

A: We know that,

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

A: The volume of the cylindrical shell is given by V=2πrh∆r, where ∆r is the thickness of the shell.…

Q: The radius and height of a right circular cone are measured with errors of at most 1% and 4%,…

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Q: A force of 7 lbs is required to hold a spring stretched 0.5 ft beyond its natural length. How much…

A: Question is solved.

Q: A linear density of a rod of length 16 m is given by p(x)=25sqrt x+4 measured in kilograms per…

A: In the question it is asked to calculate the value of x at which when the rod is cut, two pieces of…

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

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Q: A closed rectangular box is to have an inside length of 8 meters, an inside width of 5 meters, an…

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

Q: The radius of a ball is claimed to be 4.5 inches, with a possible error of 0.05 inch. Use…

A: Given that,radius (r) = 4.5 inches, dr=0.05Surface area of ball is A = 4πr2= 4π(4.5)2 =4π x(20.25)A…

Q: The edge of a cube was found to be 107 cm with a possible error in measurement of 0.03 cm. Use…

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

A:

Q: A cylinder object has radius 2 cm and height 3 cm. Use differentials to approximate the error…

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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 Approximate the volume of a golf ball using differentials if the diameter of its rubber-like core…

A: Given that the diameter of a golf ball's rubber-like core is 32 inches and  its ionomer resin cover…

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: A person measures the side of a cube as being 10 inches and thus calculates the volume of the cube…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: a steel pipe with an outside radius of 12 inches and a length of 2 ft is coated outside with 0.01…

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Q: A boundary stripe 3 in. wide is painted around a rectangle whose dimensions are 140 ft by 200 ft.…

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Q: A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

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Q: A metal chain ladder, 20 meters long, has a linear density of 3 Newtons per meter, and hangs down…

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Q: Use differentials to determine the approximate area, dA, of a circular ring which has an inside…

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Q: A capacitor has two parallel metal plates measuring 0.45 m² each. The distance between the plates is…

A: Given:-Area of plates=0.45 m2distance between plate, d=1 cm=10-2mthickness of permittivity ,…

Q: A spherical ball is measured to have a radius of 6 cm with a possible measurement error of ±0.1rmcm.…

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Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use…

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

Q: A manufacturer produces a triangular lamina with a standard base and height of 30 cm and 12 cm,…

A: we have been given the measurements of a triangle a base = 30 cm and a height =12 cm  area of the…

Q: 8. Use differentials to approximate the change in the volume of a cylinder if the height is…

A: Let's find.

Q: The diameter of a circular disk is measured as 30 cm with a maximum error in measurement of 0.2 cm.…

A: Given that :- Diameter = 30 cm , error = 0.2cm Area of circular disk = πr2 . Where ( r = d/2) So ,…

Q: The thickness of the shell is a = 0.7 centimeter. Use differentials to approximate the volume of the…

A: Volume of sphere V= 43π×r3 From given figure radius is 100 cm .

Q: The radius of a circular disk is given as  28cm with a maximum error in measurement of 0.3 cm. Use…

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Q: a hemischperical dome has a diameter of 50 m. use differentials to estimate the amount of paint…

A: the problem concerns an application of differentials

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: Suppose that you are stranded—your rocket engine has failed—on an asteroid of diameter 3 miles, with…

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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: The dimensions of a closed rectangular box are measured as 88 cm, 53 cm, and 32 cm, respectively,…

A: Given: The dimensions of closed rectangular box is : =88cm×53cm×32cm

Q: A hemispherical dome with a diameter of 60 meters has to receive a coat of 5 cm of paint. Use…

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Q: A cube with sides 14 inches long is covered with a coat of fiberglass 0.4 inch thick. Use…

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Q: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

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

A: Volume of a sphere with radius r is V=43πr3

Q: The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively,…

A: For a function y=fx, ∂y,∂x,dy and dx represents partial derivative of y and x and then differential…

Q: When a tornado passes near a building,there is a rapid drop in the outdoor pressure and the…

A: Pressure is measured as the ratio of force upon area

Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Given: length,h=20 cmd=6 cmdr=0.001dV=?

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 radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm of the disk.

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

A:

Q: 3. A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: Solved below.

Q: Use differentials to estimate the amount of paint needed toapply a coat of paint 0.05 cm thick to a…

A:

Q: The radius of a spherical ballon is measured to be 10 inches, with a possible error of 0.04 inch.Use…

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Q: A sphere is measured and the radius is 5 inches with a possible error of at most 0.02 inches.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The radius of a circular disk is given as 27 cm with a maximum error in measurement of 0.2 cm. Use…

A: