An astronaut using a camera measures the radius of Earth as 4000 mi with an error of ±80 mi. Use differentials to estimate the relative and percentage error of using this radius measurement to calculate the volume of Earth, assuming the planet is a perfect sphere.

Q: find by use of differentials the approximate total area of a right circular cone whose base radius…

A: Given : Right circular cone whose base radius and height are 5.03 inches and 11.89 inches. We know…

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 dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters, and 60…

A: Given: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters and…

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: The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch. (a)…

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Q: .A ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

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

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Q: The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use…

A: Let the length and width of a rectangle are L and W respectively. Now, The length and width of a…

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: 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: 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: 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) Use differentials to approximate the possible propagated error in computing the area of the…

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Q: Write the differential formula that estimates the given change in volume or surface. Then, use the…

A: Let y=f(x) be a differential function.  differential dx  is an independent variable.  the…

Q: An open cylindrical tank is to have an outside coating of thickness 2cm. If the inner radius is 6cm…

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Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: Given: The edge of a cube, x=30 cm The error in measurement, ∆x=0.1 cm

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

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: 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 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 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: The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the…

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Q: Suppose the measurement of the side of a square is to be 30 cm with an error of 0.03 cm. Use…

A: Definition used -      Error in area of the square -                 ∆A=2x∆x          Here x is…

Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: To find out the relative error in the lateral surface area of the cylinder.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of.1 cm. Use…

A: Consider the edge length of the cube is a , so the volume of the cube is: V=a3 The surface area of…

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: The radius of a circular manhole cover is estimated to be 16 in. with a maximum error in measurement…

A: Due to our guidelines I am solving only first problem  The radius of circular manhole r = 16 in

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 measurement of the radius of the end of a log is found to be 5 inches, with a possible error of…

A: Given : Radius of end of log is 5 inches. Possible error ½ inches The end of log is in the shape of…

Q: The altitude of a certain circular cone is the same as the radius of the base, and is measured as 5…

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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: 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: 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: The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. Use…

A: Topic = Derivative

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

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

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Q: The Spicee Pepa’Roni Pizza Company serves large circular pizzas with a diameter of 18 inches. Use…

A: Diameter of circular pizza is 18 inches and the diameter has a measurement error of +- 0.050…

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…

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Q: The radius of a circular disk is given as 28 cm with a maximum error in measurement of 0.2 cm. Use…

A: Write the expression for the area of the circle and take the derivative.

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…