The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in comuting (a) the volume of the cube and (b) the surface area of the cube.

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 length, width, and height of a rectangular box are measured with an error of at most 5%. Use a…

A: Differentiate diagonal and use error

Q: A circular plate is measured to have a diameter of 3.5 feet if the measurement could be off by as…

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

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: The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively,…

A: Given formula for the volume of the cone is V=πr2h3 Now, the total differential of V can be…

Q: Each side of an equilateral triangle measures 3 cm, with a possible error of 0.1 cm. Using…

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

Q: The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.…

A: Let ‘x’ be the edge of cube. Then

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

A: Let the volume of the rod be V Radius of the rod be R and length be L Given: L=20cm; R=3 cm…

Q: the circumference of a sphere was measured to be 100 mm with a possible error of 0.4 cm. use the…

A: The circumference of a sphere with radius r is  given as C = 2 π r  and the surface area is given by…

Q: The side of an equilateral triangle was measured to be 233 cm with at most possible error of 0.5 cm.…

A:

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

A:

Q: ! The circumference of a sphere was measured to be 80.000 cm with a possible error of 0.50000 cm.…

A: Area of Sphere = 4πr2  circumference of sphere= 2πr  r = radius of sphere

Q: 5. Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick.…

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

A: Given that the side length of a cube is 5 cm with an accuracy of 0.1 cm Volume of a cube=side…

Q: The possible error involved in measuring each dimension of a right circular cone is + inch. The…

A: The propagated error dV = V'(r)dr, here dr = +0.1 or -0.1 inch and r = 4 inches.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.l cm. Use…

A: Let the edge of the cube be x= 30cm And given error in measurement of edge dx= 0.1cm a) Volume of…

Q: The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm. (a) Use…

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Q: For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included…

A: Concept: Estimating error using differentials: ∂A=∂A∂a∂a+∂A∂b∂b+∂A∂θ∂θ Here A is the area of the…

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

A:

Q: The diameter of a spherical ball bearing was measured to be 7.8 mm with a possible error of 0.07 mm.…

A:

Q: The measurement of the side of a square floor tile is 16 inches, with a possible error of 86 nch Use…

A: we know the area of square is x^2.

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…

Q: A coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 30…

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

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 dimensions of a closed rectangular box are measured as 97 cm, 60 cm, and 30 cm, respectively,…

A: Let the dimensions of the box be l, w and h (for length, width and height).Surface area of the box…

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm. By the…

A: The radius of a circular disk is measured as 24cm with a maximum error of 0.2 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: 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: 4. The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32…

A: topic - differentials

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

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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 radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a)…

A: Solution:

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

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

A:

Q: the radius of a circular manhole cover is estimated to be 16 inch with a maximum error in…

A: The radius of the circular cover is given as, r=16 inch The error in the radius is given as, ∆r=0.06…

Q: (b) Use differentials to estimate the maximum error in the calculated volume. What is the relative…

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

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Q: 1. The edge of a cube was found to be 32 cm with a possible error in measurement of 0.1 cm. Use…

A: Given : Measurement of edge of cube a = 32 cm Possible error in measurement of edge is da = 0.1 cm…

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

A:

Q: The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use…

A: The given data is: Edge of the cube x=15 cmPossible error dx=0.2 cm

Q: A conical glass, 10cm high and 8cm in diameter at the top is filled with an exquisite wine to a…

A: Find the sum of volume of the wine and ice cube and compare with the total volume of the conical…

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

A: