A sphere is measured and the radius is 5 inches with a possible error of at most 0.02 inches. Determine the approximate error( using differentials) in computing the volume of the sphere. (V = (4/3) tr*).

Q: An engineering instrument is able to measure the side of a square to within ±0.05 mm (dr). First,…

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

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

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

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: he measurements of the base and altitude of a triangle are found to be 38 and 42 centimeters,…

A: The solution is :

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: 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: 1) The length of the edge of a cube was measured to be 30 cm with a possible error in mea- surement…

A: Given:- The length of the edge of a cube was measured to be 30 cm with a possible error in mea…

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: The dimensions of a closed rectangular box are measured as 93 cm, 66 cm, and 50 cm, respectively,…

A: Given,           The dimensions of a closed rectangular box are measured as 93 cm, 66 cm…

Q: A company manufactures spherical ball bearings of radius 3 cm. The customer requires a tolerance of…

A: Given data is : Radius r=3 cm Tolerance is no more than ±1% , therefore dr=±1%

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

A: The solution are next step

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: 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: Recall that the volume of a right circular cylinder of radius r and height h is V = r’h. Suppose…

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Q: The radius of a circular disk is given as 24 cm with a maxi -mum error in measurement of 0.2 cm.(a)…

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 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.…

A:

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

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Q: Use differentials to approximate v410, and then compare your approximation with the actual answer…

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

A: Let's find.

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 sphere is measured and found to be 3 ft. with a maximum error of 0.1 in. Find the…

A: The solution of the problem is given in the next step.

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: The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter. (a)…

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Q: Find the approximate surface area of a sphere of radius 5.02 cm. (SOLVE BY USING DIFFERENTIAL…

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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: 7. The raidus of a circle is equal to 4m and is measured with an error of ±0.5m. Use differentials…

A: Given: The radius of the circle is 4m and with an error ±0.5m To find the relative error ∆AA≈dAA "As…

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

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Q: The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using…

A:

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

A:

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

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

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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 relative error in the lateral surface area of a right circular…

A:

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

A: (a).            Volume of cube :                       V  =  x3                      dV  =  3 x2…

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

A:

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.