Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about the x-axis.

Q: Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with…

A:

Q: Compute the surface area of revolution about the ?-axis over the interval [0,?] for ? = 6sin(?).

A:

Q: Find the surface area of the solid obtained by y=2x, 0sx58revolving around the x-axis

A:

Q: Use a computer algebra system to find the approximate surface area of the solid generated by…

A: To find the surface area using the computer algebra sysytem

Q: Find the area of the surface obtained by rotating the curve about the y-axis. x=y^3, 0 less than or…

A: Consider the given curve and draw it,

Q: Find the volume of the solid cut from the thick-walled cylinder 1 ≤ x2 + y2 ≤ 2 by the cones z =…

A:

Q: Find the surface area of revolution about the x-axis of R.

A: Given curve y=2x, 2.3≤x≤4.2 We have to find the surface area of revolution.

Q: Find the surface area of revolution about the y-axis of y=6x+3 over the interval 0 ≤ x ≤ 3

A:

Q: Find the area of the surface generated by revolving the region bounded by, y6 1 x = + 16y4 i 1<ys 5…

A: In this question, we find the surface area generated by rotating the region bound by the given curve…

Q: Find the volume of the torus generated by revolving the circle (x - 2)^2 + y^2 = 1 about the y-axis.

A: Given: (x-2)2+y2=1

Q: Compute the surface area formed by rotating the portion of the curve in the first quadrant about the…

A: Given curve is x=(cost)(1+cost),y=(sint)(1+cost) , 0≤t≤2π Differentiate with respect to t.…

Q: Find the surface area generated by revolving x=sqrt(8y-y^2) about the y axis on the interval: y=…

A:

Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: Find the area of the surface generated by revolving the region bounded by, 1 1syss 16y4 y6 1<y< 5 6.…

A:

Q: Calculate the surface area x2+y2+z2=25, between the z=1 and z=4 planes

A:

Q: y = } + sxs1 <x<1 2

A:

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: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3  on 0, 1 about x-axis. This implies that,…

Q: Find the surface area if C = {(x, y): 1 ≤ x ≤ 2,y = about the x-axis.

A:

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 2≤x≤5

A:

Q: Q3: Develop the lateral surface of a hexagonal prism of base edge 20mm a on its base on HP such that…

A: Given: To explain the given statement as follows, To develop the lateral surface of a hexagonal…

Q: Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=6 about the…

A:

Q: Find the surface area obtained by rotating x = 3t2, y = 2t3, 0sts 3 about the y-axis.

A:

Q: Q10 Find the area of the surface generated by revolving the region bounded by, x6 1 y =6+ 16x4 1<x<3…

A:

Q: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: If the curve y = 4x², 2 ≤ x ≤ 5, is rotated about the x-axis, what is the integral that represents…

A:

Q: Find the area of the surface generated by revolving x = 6t and y = 4ť (0 < t < 1) X

A: answer is in next step

Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

A:

Q: Find the area of the surface obtained by rotating the region formed by 1 In x, 1<x < 2, - 2

A:

Q: Find the surface area generated by rotating the portion of the curve x-y = 0 from x 0 to x = 2 about…

A: We have to find surface area

Q: 7 Find the area of the surface generated by revolving x = 2/4-y, 0sys about the y-axis.

A:

Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

Q: Find the area of the surface generated by revolving x=t^2      y=2t.     t∈0,4) around the x-axis

A:

Q: Find the surface area of revolution about the x-axis of C.

A:

Q: Find the area of the surface generated by revolving the curve y = 3sqrt(x)  between x = 0 and x = 4…

A: Given curve, y=3x x = 0 and x = 4

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Find the surface area of revolution about the x-axis of y 7x + 7 over the interval 0 < a < 3

A:

Q: Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is…

A:

Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the surface area of revolution about the x-axis of y = 2x + 6 over the interval 2 < x < 5

A:

Q: Find the surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: By rotating the line y = r about the x-axis, for x in the interval [0, h], and applying the surface…

A:

Q: Find the area of the surface generated by revolving the region ounded by, y6 1<y< 5 6. 16y4 bout the…

A:

Q: Find the area of the surface generated by revolving the curve x = Osys2, about the y-axis

A: Given: The curve is x=y32, 0≤y≤2 about the y-axis The formula for find the area of the surface is…

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

A:

Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

A: