A right circular cone of radius R and altitude H is circumscribed about a sphere of rafius r. Find the relation between H and r if the volume of the cone is to be minimum.

Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 : = 35 and the upper cone z2 =…

A: The given problem is to find the volume of the ice cream that is bounded by given surfaces. Given…

Q: Sketch the regions enclosed by the given curves. y = Vx, y -x, x = 25 y y 8 6 41 4 2 10 15 X 25 5 20…

A: Consider the provided curve, y=x,y=13x,x=25 Sketch the region of the provided curve and find its…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30,0 < 0 <…

A: Given, r=3θ,  0≤θ≤5.4

Q: Sketch the region enclosed by the following curve and find its area. x = y^4, y =√2 − x, y = 0

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Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

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Q: Suppose a sphere of radius r is sliced by two horizontal planes h units apart (as shown). Show that…

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Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

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Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: Show that a closed right circular cylinder of given surface has maximum volume if its height equals…

A: Let, the surface area be S, radius be r, height be h and volume be V. The total surface area be…

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: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: Find the area of the region

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Q: 3. Show that a closed right circular cylinder of given surface has maximum volume if its height…

A: Let r, h be the radius and height of the cylinder respectively and V, S be the Volume and Surface…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A:

Q: he volume bounded by the function_z = f(x, y) = xy√x² - y² <10 and 0≤ y ≤8. over

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Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Consider a sphere of radius 1 situated at the origin in R³. Find the surface area of the slice of…

A: Consider the provided question, Given that, a sphere of radius 1 situated at the origin.

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

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Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z2 = 3x2…

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Q: Find the by the two curves enclosed area the two wrves y=x² and y=x²-x²- 6x corvect to 2 dec.places…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 40,0 ≤ 0 ≤…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

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Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

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Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

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Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: If ƒ(x, y) = 100 ( y + 1) represents the population density of a planar region on Earth, where x and…

A: Given: The reginal population is f(x,y)=100(y+1) And the curve is f(x,y)=100(y+1)

Q: If 0 ≤ f (x) ≤ g(x) for x in the interval [a, b], can the surface obtained by rotating the graph of…

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

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Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…

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Q: Find the volume generated if the are bounded by curve y=x^2 and the line y=2x+3 is revolved about…

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Q: Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =x, x>0 16 y y 10| 10- 8 6. 2 4…

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Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the radius of the outer disk when the region bounded by y = x^2 and y = 1 + x − x^2 is revolved…

A: We will find out the required value.

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

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Q: Sketch the regions enclosed by the given curves. y = Vx, y = Ex, x = 9 y y 5 5 4 3 3 1 1 X 2 4 6 8…

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Q: Sketch the reglons enclosed by the glven curves. y = Vx, y= X= 16 y y 6 4 4 3 3 2 10 15 10 15 O-1…

A: Given : y = √x  y = 1/3 x  x = 16

Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z2 = 10 and the upper cone z2 = 4x2…

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Q: Right circular cones of height h and radius r are attached to each end of a right circular cylinder…

A: Let Vcr be the volume of the cone and Vc be the volume of the cylinder. So, Vcr=πr2h and Vc=13πr2h.

Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.