The height and base radius of a circular cylinder are measured as 15 cm and 4 cm, respectively, with a possible error of measurement of as much as 0.5 cm each. Use differentials to estimate the maximum error in the calculated volume of the cylinder.

Q: The measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters,…

A: Let base= B  Altitude= H Given that B= 36 , H=50 , dB=0.25 , dH=0.25

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 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: 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: 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: 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: A wooden rectangular box is to be made having dimensions 3 ft, 4 ft, 5 ft. The cost of the wood to…

A: From the given information, the length, width and height is 3 ft, 4ft, 5ft respectively. The given…

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

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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 width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

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

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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: The dimensions of a closed rectangular box are measured as 80 centimeters, 60 centimeters, and 100…

A: Let the dimensions of a closed rectangular box are: Length=L=80 cmWidth=W=60 cmHeight=H=100 cm And…

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: A circle has a radius of 5 cm, if the radius is increased by 0.1 mm., what is the estimated increase…

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

A: Solution.

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

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

A:

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: 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…

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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: 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: 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…

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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: 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: 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.