The lateral (side) surface area of a cone of height h and base radius r should be πr√r2 + h2, the semiperimeter of the base times the slant height. Show that this is still the case by finding the area of the surface generated by revolving the line segment y = (r/h) x, 0 ≤ x ≤ h, about the x-axis.

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y =x,…

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Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Find the area of the surface of revolution generated by revolving the curve y = 5/ 0Sa<4, about the…

A: Given that:  y=5x,                        0≤x≤4

Q: A right-circular cone is to be circumscribed about a sphere of given radius. Find the ratio of the…

A: Let R be the radius of the cone, l its slant height and h be the height. V= 13πR2h We have to make…

Q: Use the integral table and a calculator to find to two decimal places the area of the surface…

A: Consider the given equation of the curve y = x2,  -1 ≤ x ≤ 1.The surface area of the surface…

Q: Find the area of the surface generated by revolving the curve y = sqrt(x2 + 2), 0…

A: find dy/dx and solve for ds.

Q: Find the area of the surface obtained by revolving the curve given by y = V/9- x2, where –2 < x < 2,…

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Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by…

Q: 3) Find the area of the surface obtained by rotating the given curve about the indicated line, y=x2,…

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Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: Find the area of the surface obtained by rotating the curve V5=x' 3 Sx 55 about the x-axis a

A: Here function is, y = (5-x)^(1/2) Since function is positive for the given interval and has a…

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: The frustum of the cone of revolution is 5ft high and the diameters of its bases are 2ft and 3ft,…

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Q: Find the lateral surface area of the cone generated by revolving the line segment 5x – 8y + 40 = 0,…

A: 5x-8y+40=0

Q: A cone with radius 5 and height of 10 is intersected herirontally by a plane. At the point of…

A: Given data, Radius of cone, R = 5 units Height of cone, H = 10 units A plane is intersection…

Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x², -2 <x<2 about the x –…

A: Let's find.

Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x/2, 0…

A: The given line segment is y=x2 where 0≤x≤4. The line segment is revolved around x-axis, thus it…

Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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Q: Find the length of the curve y =Vx³, for [0, 4]. Find also the surface area of the region is rotated…

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Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x2, -2 < x<2 about the x -…

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Q: Find the surface area of the solid gained by revolving the curve 0 < x < 14, about the x – axis. 14'

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Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V 25 - x2, 0 sx< 4,…

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Q: rated by revolving the area bounded by the parabola y² = 8x and its latus rectum about the latus…

A: Introduction: The chord that passes across the focus of a parabola and is perpendicular to the…

Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

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Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Given: The equation of the curve is The region is rotated about x-axis. The volume of solid…

Q: Find the lateral surface area of the cone generated by revolving the line segment 5x – 8y + 40 = 0,…

A: Given problem is :

Q: The volume of the solid generated by revolving the curve x = 4, about the y-axis between y= 0 and y…

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: Find the area of the surface of revolution generated by revolving about the x-axis the arc of the…

A: y2=12x ⇒y=23x ⇒dydx=3x ⇒dydx2=3x2 ⇒dydx2=3x ⇒1+dydx2=1+3x ⇒1+dydx2=1+3x

Q: A flat, very thin table has a circular hole with radius 1 and a circular hole with radius 2. The…

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Q: y = x, 0 < x <7

A: The given line  y = (7/5)x This is revolved about x axis  0≤x≤7

Q: 135 Find the area of the surface generated by revolving x = 4V9 - y. 0sys- about the y-axis. 16

A: Solution

Q: Find the volume, V, of the solid formed, when the part of the curve y = 2x, is rotated about the…

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Q: Find the area of the surface obtained by rotating the following curve about the x-axis. y=2x3 , 0…

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Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: Given that, the cone is generated by revolving the line segment  y = 53x,  0≤x≤4, about x-axis.

Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

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