The radii of the bases of two right circular solid cones of same height are r1 and r2 respectively. THe cones are melted and recast into a solid sphere of radius R . show that the height of each cone is given by h =((4R3)/(r12+r22))

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Use the error bound for the trapezoidal rule to find the smallest N such that the error in…

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Q: A tank full of cooking oil has the shape of a paraboloid obtained by rotating a parabola about the…

A: We have given a paraboloid tank full of cooking oil. Height of tank = 4m. Radius at its top = 4m. We…

Q: Find the area of the surface. The portion of the cone z = 4V+ y² inside the cylinder x? +y² = 16

A: Consider the provided cone z=4x2+y2 inside the cylinder x2+y2=16. Find the area of the surface. The…

Q: * = Vy +5,

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

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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Q: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

A:

Q: The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and…

A: If the area of the sector is 1 sq. unit, then A=112r2θ=1θ=2r2          ...(1)

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 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 revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: If N is a sphere of radius R that is centered around the origin. Use appropriate functions and…

A: Simplify the integral:  ∫Ωr→r3∇→r4-R4r5+7r3+2dτ=∫Ωrr3r^r^ddrr4-R4r5+7r3+2r2sinθdrdθdϕ…

Q: A point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt…

A: We have to show  that the length of this arch is always four times the diameter of the rolling…

Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: H use spherical Cingidinates to find the velumi of the oliet inside xtty42²=9 and outside z=ty" and…

A: Given sphere, x2+y2+z2=9 outside z=x2+y2   and above xy plane. We use spherical coordinates to find…

Q: Find the olume of the solid cut Prom the sphere 8=2C@SQ by the Cone Z= Jx+ ý Ans/ T

A: The given question is related with triple integral. We have to find the volume of the solid cut from…

Q: The lateral (side) surface area of a cone of height h and base radius r should be Ar v? +h?, the…

A: Consider the provided question, Given the line segment, y=rhx,  0⩽x⩽h Differentiate both side of…

Q: The uniform rod weighs 420LBa and has its center of gravity at G. Determine the tension in the cable…

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Q: Find the uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

Q: The total surface area of a cone with radius x and slant height 3x is equal to the area of a circle…

A: Solution:-The total surface Area of cone=πrl+πr2    radius=x    slant height=3x⇒πr3x+πr2…

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

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Q: The lateral (side) surface area of a cone of height h and base radius r should be πr√r2 + h2, the…

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Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 %3D and…

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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: Find the area of the surface generated by revolving the given curve about the x-axis. y = V9 -x,…

A: 3

Q: ind the area of the surface generated when the give curve is revolve about the x-axis    y=(x^3)…

A: Consider the given curve: Here the objective is to determine the area of the surface generated when…

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

A:

Q: (b) Consider the cycloid C parametrized by x = t – sin t and y = 1 – cos t, for all real t. Find…

A: Solution x= t-sint, y =1-cost C(0) = (0,0) C(pi) = (pi-sin pi, 1-cos pi) = (pi, 2) C(2pi) = (2pi-0,…

Q: Find the length of the radius r of a right circular cone with l = 12 in. and h = 3r in.

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A: Given data:  The radius of the circle is "R". The equation of circle with radius "R" is given by…

Q: Find the average z-coordinate of points in a hemisphere of radius 8 centered at the origin with its…

A: We have to find the average z coordinate of the hemisphere of radius 8 centered at origin with base…

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: The volume V of a cylinder of height 4 cm and radius r is given by: V = 4ar? What is the…

A:

Q: Find the length and the cuur vature of the Smooth eurve rCt) = (snt)i t(5 cost); + (sint)K from o to…

A: Given curve is rt→=sinti+2costj+sintk and given t from 0 to 2π We have to find the length and…

Q: Which integral computes the circumference of the ellipse + y° = 1? %3| 2 16 — За? dx 16 — 4г2 2 -2 2…

A: As we know the differential arc length of a curve is ds=dxdθ2+dydθ2dθ  The parametric equations of…

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

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Q: Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) =…

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Q: Prove that the surface area of a sphere with radius r is given by S = 4r? using the methods of this…

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Q: Find the average x-coordinate of a point on the half-torus with the following parametrization (drawn…

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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: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

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Q: A fence of height H is D feet away from a vertical wall. At what angle θ should a ladder be leaned…

A: Figure

Q: Find the average distance from a point P(x, v) in the first two quadrants of the disk x2 + v s25 to…

A: We have a given point P(x, y) and a disc   x2+y2≤25 We need to calculate the average distance from…

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.