A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21 cm. Use differentials to find the approximate amount of paint required for the job, correct to the nearest cubic centimeter.

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 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: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.06 cm…

A: Given information: The diameter of the hemisphere is 52 m that means the radius is 26 m. Formula…

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: 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 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: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

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: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

A:

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: 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…

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

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: 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…

A:

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

A: Let's find.

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 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: 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: A square is measured and each side is found to be 8 inches with a possible error of at most 0.01…

A: We are given that each side of a square is 8±0.1. Let x be the side of square and then the side of…

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: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

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

A:

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 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: 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 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 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: 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 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: Use differentials to estimate the amount of metal in a closed cylindrical can that is 18 cm high and…

A:

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

A:

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

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

A:

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: 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: 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: