Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal to 2507. Calculate m.

Q: Let V be the volume of the solid obtained by re

A: Given, the curves                  y=x,  y=x2

Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: Use the Theorem of Pappus to find the volume of thegiven solid.52. A sphere of radius r

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Q: Find the volume of the solid generated when R is revolved about the given line. -E,y-1, and x- | , a…

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Q: 5. Find the volume of the solid enclosed by z = 4, y = 0, y = 25 – x2, and z + y = 29.

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Q: Find the volume generated by rotating the given region about the specified line. R, about AB

A: On revolving the region R1 around the line Ab, the resulting solid obtained will be a cone.   This…

Q: Find the volume of the solid S whose base is the disk bounded by the circle x^2 + y^2 = r^2 and the…

A: Solution is given below:

Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

A: We will first find the area of cross section. Then integration of Area will be required volume of…

Q: Find the volume generate by rotating the given region about the specified line. R2 about BC

A: Integrating a small volume element within appropriate limits will result in the complete volume of…

Q: Find the volume of the solid bounded by: æy = 2, y = 0, æ = 2, and a = 4 a. about x = 1

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Q: Find the center of mass for the specified area between the pieces Equivalent y=x^2/b and straight…

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

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Q: Find the total mass of the triangular region in the figure below, which has density 8 (x) = 2 + x…

A: According to the problem , we have

Q: Find the volume of the solid in R' bounde y = x², x = y² , z = x + y + 33, and z V =

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Q: Find the volume and the surface area of a “closed boOx' that has dimensions of 15 cm, 20 cm, and…

A: Given that: The dimensions of a " closed box" are 15 cm , 20 cm and 0.25m. 1m = 100 cm

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

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Q: Find the total mass M of a 2-m rod of linear density ρ(x) = 1 + x(2 − x) kg/m, where x is the…

A: Consider the given given information. ρx=1+x2-x kg/m   The mass of the rod is given by the formula.…

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: Compute the volume lying inside the sphere x2 + y? + z2 = 46 but outside of x² + y? = 21.

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Q: For the area bounded by y2=4x and y=x, find the volume generated if it is revolved about the line…

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

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Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

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Q: Describe a region whose volume is equal to: (а) 27 | p² sin o dp dộ dô Jo (b) /4 2 rdr de dz -2 J7/3…

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Q: Compute the volume lying inside the sphere x2 + y? + z2 = 35 but outside of x² + y? = 19.

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Q: Calculate the total mass M of a circular piece of wire of radius 4 cm centered at the origin whose…

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Q: Find the volume in the first octant bounded by the cylinder x² +y = a² 2a and the lane z = x + v.

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Q: Find the volume of a stereoscopic body by rotating a given straight line around an axis surrounded…

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: calculate the volume of G where G is bounded by 2= x² + y²₁ ²²+ y² = 4, 200 SS f d v

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Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

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Q: Determine the diameter of a closed cylindrical tank having a volume of 11.3 m? to obtain a minimum…

A: Formula: Volume of cylinder: πr2h Surface are :2πrh +2πr2

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

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Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

Q: Find the volume of the solid which is (a) bounded by x+ y+z = 4 in the first octant.

A: As per our guidelines we are supposed to solve only one question. For the solution follow the next…

Q: Find the mass of a solid ball of radius 1, if the density at each point r units from the center is…

A: Given density at each point r units from the center of the ball is 11+r2.

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: 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: use the disk method to find the volume (in units^3) when the regionbounded by the curves x+y=5, x=0,…

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Q: Find the volume enclosed between the two surface :z x + y and z=3

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Q: Calculate the volume of solid Q limited by surface z

A: Consider the solid Q: Clearly, 0≤z≤11+x2+y2Let x= r cos θ       y=r sin θ⇒x2+y2=r2Projection on the…

Q: Compute the ”volume” of the 4-dimensional unit ball, which is the area enclosed by the equation x^2…

A: The equation of four dimensional unit ball is x2+y2+z2+w2=1 Volume of ball is equal to…

Q: Suppose a solid mass is in the shape of the unit ball in R³, that is, the region with ² +y? + 2? <…

A: We are given the region is x2+y2+z2≤1. And the mass density of the solid mass is fx, y,…

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: For a right circular cylinder, suppose that r= 6 in and H=7 in. Find the exact: Volume

A: Given Radius (r) = 6 in Height (h)=7 in To find Volume of right circular cylinder

Q: Find the center of mass defined as the area between the parabola Y = x/b and the line Y =b y = b

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Q: Find the mass of a circular cone of height b and radius of base a whose density varies as the…

A: To find: The mass of a circular cone. Given information: The height of the cone is b and base is a…

Q: Show that the volume of the region bonded by the cone z=/x +y and the paraboloid z x+y is a/6.

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Q: The volume of the solid generated by revolving the curve x = , about the y-axis between y = 0 and y…

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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.