Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about y-axis from 5≤ y ≤ 10. Verify your answer with the geometric formula for the lateral surface area of th right circular cone.

Q: Find the area bounded by the curve 4 square units O 16 square units O 8 square units 10 square units…

A:

Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: It is given that, y=16x2y=9   Area under the bounded region can be calculated by using,…

Q: Estimate the length of the curve y=0.5x² over [1,4] using n=6 and trapezoidal method. Also determine…

A: In trapezoidal rule the value of a interval is computed by ∆x=b-an. In the above formula a is the…

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

A:

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

A: Given equation of line segment is  y = x/2, 0 ≤ x ≤ 4,

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

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: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

A:

Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

A:

Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

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: Find the area of the segment cut off from the curve y = sin x, 0≤x≤ n by the line y = 1/√2. H4 34 y…

A: Let's find area of segment.

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: 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: Q2. For a cone having surface area of (S = 850 cm²), the radiusestimated using secant method with…

A: Given that cone having surface area. So, f(r)=πrr2+h2-850 Since the height is not given. So let's…

Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

A:

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x² between…

A: Solution: Consider the given curve y = x2 The curve revolving between x = 1 and x = 2 about the…

Q: Find the area of the surface generated by revolving the curve y = 2x -x² , 0.25 sxs0.75, about the…

A:

Q: gion shaded in light blue is bounded by two curves, y = (x – 1)? + 33 (in dark red) and z+ 3)² + 1…

A: We will find the area between the curves.

Q: Find the area of the surface oblalned by rotating tne curve y = V4x x = 0 to x = 3 about the x-axis.…

A: Below is the solution:-

Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

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 area bounded by the curve 16 square units 10 square units 8 square units 4 square units 16…

A: The region is bounded by y=116x3-34x2+3x and the line y=x.

Q: Find the area of the surface obtained by rotating the curve y = √(5-x),   3≤x≤5 about the x-axis.

A:

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

A:

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

A:

Q: Find the number b such that the line y = b divides the region bounded by the curves y = 9x² and y =…

A: Given, The curves are y =9x2 y =25 y = b Let's draw the curve y =25 and y = b are straight lines…

Q: Find the area of the surface generated by revolving the curve y = - V6 sxs0, about the x-axis. 24'

A:

Q: Find the surface area generated by revolving y=5x+2 about the x axis on the interval [0,6]

A:

Q: Find the area of the surface generated by revolving the curve Y = 8/x, 2 < x < 7 around the -axis.

A: The given surface is generated by y=8x,  2≤x≤7 around the x axis. The area of the surface generated…

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

A:

Q: Estimate the length of the curve y=0.5x² over [1,4] using n=6 and trapezoidal method. Also determine…

A:

Q: Find the area of the surface generated by revolving the curve y =2x-x, 0.5sxs1, about the x-axis.

A: To calculate the area of the surface we use the formula A=2π∫abf(x)1+((f'(x))2 dx

Q: Find the area of the surface generated by revolving the curve y = sqrt 2x-x^2, 0.25 less than or…

A:

Q: Find the area of the surface generated by revolving the curve: y = V4 -x, -1sxs1 about x-axis.

A: The given curve is: y=4-x2,-1≤x≤1 about x-axis. The formula of surface area=∫ydx

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 enclosed by the closed curve obtained by the joining the spiral r=4θ by a straight…

A: Given that, the value of r=4θ and θ∈0,1.7. It is known that, the formula for the area of the…

Q: The area under the curve 4y2 =" (x2 + 1)3 was rotated about a line located to the left of y – axis…

A: The surface area of the solid can be obtained using the Pappus theorem. The surface area is…

Q: Find the area of the surface generated by revolving the curve y = Osxs2, about the x-axis. 9

A:

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: Find the area of the surface formed by revolving the graph of y = 2Vx on the interval [0, 14] about…

A:

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: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

A:

Q: Find the area of the surface generated by revolving the curve y=2/x 18xs2, about the x-axis.

A:

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

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.