Suppose a l-m cylindrical bar has a constant density of 1 g/cm for its left half and a constant density 2 g/cm for its right half. What is its mass?

Q: A solid cylinder has a radius of 4 cm and a height of 10 cm. The cylinder is made from wood and has…

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Q: A thin 8 cm wire represented by 2 < x < 10 has density function p(x) = xVx? + 1g/cm. Find the mass…

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Q: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…

Q: An inverted conical tank with a height of 6 m and a base radius of 1.5 m is filled with milk, which…

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Q: The length of a rod is 4 meters and the linear density is (3/4)x + 2 kg/m from any point x from one…

A: Center of mass is defined as a point in space where the weighted relative position of the…

Q: Find the moments and center of mass for the thin plate covering the region between the x-axis and…

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Q: in the first quadrant. Find its center of mass if the density at any point is proportional to its…

A: D=(x,y):0≤x≤11, 0≤y≤121-x2 And f(x,y)=ky  [k is constant of proportionality] converting to polar…

Q: 2. The length of a rod is 20 cm and the linear density of the rod at a point x centimeters from one…

A: Consider that the length of the rod be 20 cm and its density is D(x)=3x+2 g/cm. Find the total mass…

Q: Find the approximate formula for the volume of a thin spherical shell.

A: Consider two spheres centered at the origin with an inner radius r and outer radius r+dr.  Therefore…

Q: 3. What is the volume if a cylindrical tank whose lateral surface area is 15.8 m² and whose base…

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Q: A closed right circular cylindrical tank made of s inch thick metal has an outer radius of 2 ft and…

A: solution:-(1)outer radius, r=2 ftheight, h=6 ftouter surface area of cylinder= 2πrh+2πr2…

Q: A wire takes the shape of the semicircle x2+y2 =1 y&gt;0 and is thicker near its base than near the…

A: A wire takes the shape of wire is semicircle x2 + y2 = 1, y &gt; 0 and is thicker near its base than…

Q: Find the dimensions of a cylindrical can with a volume of 666 in^3 that minimizes the surface area.…

A: To find the dimensions of a cylindrical can with a volume of 666 in3 that minimizes the surface…

Q: A hollow sphere with an inner radius of 5cm and an outer radius of 6 cm is made of a material with a…

A: Mass of Hollow Sphere = 800.5 gram

Q: Calculate the total mass of a plate bounded by y = 0 and y = x- 1 for 1 &lt; x &lt; 4 (in meters)…

A: The plate is bounded by y = 0 and y = x-1 for 1 &lt; x &lt; 4 and the mass density id y/x kg/m2.

Q: Find the center of mass of a thin rectangular plate cut from the first quadrant by the lines x = 6…

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Q: Find the centre of mass of a uniform density equilateral trianqular sheet of side L.

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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: Find the mass of the two-dimensional object. A disk of radius 8 in with a density function of ρ(x)=…

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Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

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

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Q: A metal chain ladder, 20 meters long, has a linear density of 3 Newtons per meter, and hangs down…

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Q: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

A: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

Q: Find the mass of a ball of radius R whose density γ is proportional to the squared distance from the…

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Q: Consider this half-sphere water tank of radius 5 meters. Suppose that this tank is completely full…

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Q: Suppose a water tank has the shape of a cylinder, with a circular base. The height of the tank is 9…

A: Let height of each strip is dx.  Radius =r= 2 is constant. A strip at the x ft height, has to be…

Q: calculate the work (in joules) required to pump all of the water out of a full tank. Distancesare in…

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Q: Find the mass of the one-dimensional object. A wire that is 4 ft long (starting at x =0) and has a…

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Q: 3) Calculate the work against gravity to build a box of h=3m with a square base of side 2m made from…

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Q: What is the weight of water inside a cylindrical tube of height 2m buried in the surface? [Take…

A: Topic-Volume of cylinder

Q: 10. Find the center of mass of a thin rectangular plate cut from the first quadrant by the lines x =…

A: Given density δ(x,y)=3x+yWe need to first mass using formula:M=∬RδdAAccording to the problem, we…

Q: A thin Wire is bent into the Shape of a semicircle X² + y² = 4₁ X 70. If linear density is 3, find…

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Q: Suppose that a cylindrical tank initially containing Vo gal- Use Torricelli's law to show that the…

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Q: Calculate the work required to lift a 3-m chain over the side of a building if the chain has a…

A: Consider a segment of the chain of length ∆x that has to be lifted x_i feet. To lift this segment…

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: A copper wire in 4 mm in diameter is evently wound about a cylinder whose length is 24 cm and…

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Q: Find the radius and height of a cylindrical soda can with a volume of 354 cm3 that minimize the…

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Q: A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g / cm3, find…

A: Given:            Radius of sphere =4.9 cm.

Q: The mass of the part of a rod that lies between its left end 3 and a point x meters to the right is…

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Q: Find the center of mass of the hemisphere, if it has constant density

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Q: Find the mass and center of mass of a solid hemisphere xof radius if the density at any point is…

A: Given: The radius of the hemisphere is r. The density is directional proportional to the distance…

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 mass of the two-dimensional object. An oversized hockey puck of radius 3 in with a density…

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

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Q: A soft-drink company needs to design a cylindrical can that can hold 475 ml of fluid. What are the…

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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: A hollow sphere with an inner radius of 2cm and an outer radius of 3 cm is made of a material with a…

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…