Use differential to calculate the volume of the material needed in making a thin sphere with inner radius of 40 cm and a thickness of 0.2 cm.

Q: Apply integration technique to find the volume generated by revolving the area bounded by the…

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Q: Determine the volume of the solid formed by revolving the area bounded by y² = 4x and x²= 4y about…

A: It is given that, y2=4x⇒y=2xand4y=x2⇒y=x24   Volume of solid formed by revolving the area bounded by…

Q: Find the volume of the solid with a circular base of radius 5 whose cross sections perpendicular to…

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Q: Use cylindrical about the yaris shells to find volume, rotat ing y=0,

A: Let R be the region bounded by y=x3,y=0,x=1. Find the volume of the solid of rotation about y-axis.…

Q: Find the volume of the solid whose base is in the first quadrant bounded by y = √√7-7x, the x-axis,…

A: To find- Find the volume of the solid whose base is in the first quadrant bounded by y = 7 - 7x, the…

Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: The lateral Surface area of a right circular cone is given as A =πrh2+r2        A2 =π2r2(h2+r2)…

Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

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Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Diameter=60 meters⇒radius=30 meters                         ∵Radius is half of the…

Q: : Find the center of mass of a thin plate of constant density covering the region bonded by y = 25 -…

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Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: Find the approximate surface area of a sphere of radius 3.02 in. (Use differentials)

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Q: Use the linear approximation to estimate the percentage change in volume of a right circular cone of…

A: Let V,  r  &amp;  h be the volume, radius and height of the right circular cone respectively. Given,…

Q: Find the volume of the solid whose base is in the first and second quadrant(s) bounded by y = 32 –…

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Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about x-axis.

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Q: about the y axis, which integral below giv area?

A: Introduction: The formula for the surface area of the curve rotated about y-axis is given by,…

Q: : Find the center of mass of a thin plate of constant density & = 2 covering the given region The…

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Q: FIND THE VOLUME GENERATED ABOUT THE BY REVOLVING THE AREA ENCLOSEP BY THE CURVE x+y%= 16 9-AXIS.

A: Here we have to find the volume bounded by the area about y-axis

Q: Find the center of mass of a thin plate covering the region bounded above by the parabola y = 4 - x2…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Find the surface area obtained by revolving the parabolic arc y2=x from (0, 0) to (9, 3) about the…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Find the volume of the solid generated when the area bounded by the curve y = vx, the y-axis, and…

A: Volume is the measure of the amount of space occupied by a closed surface. It is measured in terms…

Q: The closed right circular cylindrical can of smallest surface area whose volume is 686r cm³ has a…

A: Topic = Mensuration

Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

A: Your problem was not so clear. There are two different functions, the graph is not matching with the…

Q: Find the volume generated by revolving one arch of the curve y = sin x about the x-axis.

A: Let the bounds of one arch of the sine curve be 0 and pi. Then, the volume generated by revolving…

Q: Find the volume of the solid with a circular base of radius 4 and the cross sections perpendicular…

A: Given, the radius is 4 so we can conclude x2+y2=4 (equation of circle) =y2=4-x2 y=4-x2 one side of…

Q: Find the volume of the solid generated by revolving the curve y=3vx between x = 0 & x = 3 about the…

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Q: : Find the volume of the solid generated by revolving the shaded region about the x-axis: y = sinx…

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Q: What are the differential length, surfaces and volume for Cartesian coordinate system.

A: The question is taken from the Vector Calculus, and we have to give the answer the explanation for…

Q: Use cylinder shell method to graph and find volume: y=sqrt(x), y=0, x=1, about x=-1

A: If a region is bounded by a curve y=fx and x-axis on the interval a,b and it is rotating about a…

Q: Find the volume generated by revolving about the line x=0 the area under the arch of the sine curvey…

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Q: Determine the volume generated when the area bounded by the curves y-sinx and y%3cosx from x-0 to…

A: Aim: We need to find the volume of the solid obtained by revolving the bounded region (light yellow)…

Q: What is the surface integral in m2 of a long thin wire with circular cross section, length…

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Q: The radius of a circular disk is given as 20 cm with a maximum error in measurement of 0.4 cm. Use…

A: Given: The radius of a circular disk is 20 cm ie., r = 20 cm  error in measurement is 0.4 cm ie., dr…

Q: Find the center of the mass of a thin plate of constant density 6 covering the region bounded by the…

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Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

Q: Find the volume generated when the area bounded by the curve y2=x , the line x=4 and the x-axis is…

A: Volume bounded by the curves, about y-axis.using Disk method

Q: Determine the volume generated when the area bounded by the curves y-sinx and y=cosx from x=0 to…

A: Solution :-

Q: Sketch the area bounded by the function y = x^2 + 1 and the line y = 5, and then calculate the…

A: Volume of revolution

Q: What is the differential form for the total surface area of a frustum of a cone with l as the slant…

A: The curved surface area of a frustum of a cone is:

Q: 3. Use differentials to approximate the volume of a spherical shell whose inner radius is 5 cm and…

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Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A: According to the given information it is required to find the dimension of right circular cylinder…

Q: A rectangular plate 0.6 m wide and 1.2 m deep lies within a water body such that its plane is…

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Q: 2. Determine the approximate volume of a cube whose edge is 19.95 cm, using differential. 3. Use…

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Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x+ about the y-axis.

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Q: Find the volume of the solid formed by rotating the region between the y=sqrt(x)curve  y=2 line and…

A: The volume of the solid of the revolution can be calculated using integration. The formula for the…

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

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Q: The linear density of a rod at a point a centimeters from the left end is, where the left 2 grams…

A: Here, the objective is to find the mass and center of mass of the rod.