Find the dimensions of the closed right circular cylindrical can of smallest surface area whose volume is 16π cm3.

Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: Find the exact volume of the solid of revolution that results when a semicircular region with…

A: We know that if as semicircle is rotated about diameter then resulted figure will be sphere, whose…

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

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Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: Find the volume of a cap of a sphere with radius 50 and height h = 3.

A: volume of sherical cap with radius given r=50 and height=3

Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for…

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Q: Find the volume of the solid generated by revolving the area of a circle (x − 2)² + y² = 4; about…

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Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Find the volume of a solid where the base of the solid is  a circle with radius 2, and the cross…

A: Let the circle be centered at origin and the radius is 2.

Q: 8. Find the volume of the solid whose base is the semicircle y = V9 – x², where -3 sIS 3, and whose…

A: This question is based on application of integration.

Q: y = 9x² and y = 0 = about x = -4

A: First we plot the graph of the region and axis of revolution.

Q: 3. Determine the dimensions of the right circular cylinder, with the greatest volume, that can be…

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Q: Find the volume of the tetrahedron bounded by 2x−y+z = 4 and the coordinate planes.

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Q: Find the volume of liquid needed to fill a sphere of radius R to height . R y

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Q: Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal…

A: • To solve this problem, we have to express the total surface area of the cylindrical can in a…

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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Q: 5. Find the volume of spherical wedge formed by rotating through an angle of 45 a semi circle of…

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Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: A rectangle has dimensions of 6 in. by 3 in. Find the exact volume of the solid of revolution formed…

A: Given that, Rectangle with Dimensions of 6 in by 3 in.   If we rotate this rectangle then it forms…

Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y² – 2x² + 3 and above…

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Q: Find the volume of the solid generated by revolving the area of a circle. (x-3)²+y²=9; about the…

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Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

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Q: Suppose that a semicircular region with a vertical diameter of length 4 is rotated about that…

A: Given: A semicircular region with a vertical diameter of length 4 is rotated about the diameter. To…

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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Q: Find the volume of the solid whose base is the semicircle y = √4-2 where -2 ≤ x ≤ 2, and the cross…

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Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Given parabola equation is  y2=xTake square root on both sidesy=x Now we find area of square shaped…

Q: Find the volume of a right spherical segment of 2 bases if the radius of the sphere is 10 in.; the…

A: To find the volume of a right spherical segment of 2 bases. If the radius of the sphere is 10…

Q: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: The base of a solid circular with a radius of 4 cm. Determine its volume if every plane…

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Q: For a cylindrical can (depicted in the figure, height h and radius r) with volume 2π m³, compute the…

A: Surface area = 2πrh+2πr2 Volume =πr2h = 2π

Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: Calculate the mass of the solid, in the first octant, bounded by the coordinated planes and the plan…

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Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Volume of the solid obtained by revolving y=f(x) between x=x1 and x=x2 about x-axis  is,…

Q: Find the volume of a sphere. 4/3piR^3 using cylindrical shells

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Q: Find the volume of the washer that is obtained when the shaded area is rotated about the x-axis. ry…

A: Given that y=x+2,y=2 The formula for washer method is, V=π∫abf(x)2-g(x)2dx Here in the problem,…

Q: Find the volume generated by revolving the area bounded by the parabola x2 = 4y and its latus rectum…

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the volume of the wedge cut from the first octant by the cylinder x2 + y2 = 1 and the plane 2x…

A: To find the limits of x, y and z from the region of integration, substitute 0 for y.…

Q: Derive the equation for the volume of a sphere of radius r using the shell method.

A: Consider a circle of radius (r), which when rotated around x-axis generates a sphere.

Q: Find the volume of a sphere with a surface area of 900x in. The volume is in. (Type an exact answer…

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Q: Find the exact volume of the solid of revolution that results when a rectangular region with…

A: Given data: When the rectangle is rotated about its length then the revolution gives the right…

Q: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: 1. Find the volume of the solid that results when the shaded region is revolved around the Y - AXIS.…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: What is the volume, in cubic units, of the rotating body formed by rotating the region bounded by…

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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.