Let m be the least possible surface area of a closed circular cylindrical can whose volume is equal to 4327. Calculate m.

Q: Find the volume of the following solid bounded by two paraboloids. laces

A: In this question, we find the volume bounded by two surfaces. Here first we use the integral to find…

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

A:

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

A:

Q: Show by integration that the volume V of a right circular cylinder with base radius r and height h…

A:

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: Define as the region bounded by the functions u(y) = 2 and v(y) around the y-axis, what is the…

A: The region Q is bounded by the function u(y)=2 and vy=y24 between y=1 and y=2 The solid formed by…

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

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

A:

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 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: Calculate the volume generated by the circle x^2 + y^2 -4x=-3 that revolves around ox

A:

Q: Find the volume obtained by rotating R about the line = -e.

A: Volume : π2e2+4e+1

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

A:

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

A:

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

A:

Q: A spherical volume charge with a radius of 6cm has a charge density of 10 nC/m³. The total charge in…

A: The radius of the sphere r=6 cm=0.06 m Charge density ρ=10 nC/m3=10×10-9 C/m3 We have to find the…

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

A:

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

A:

Q: Let A be the area in the first quadrant bounded by the y-axis, the line y=5 x, and the line y=2…

A: Suppose a region is enclosed by two curves, y=fx and y=gx. To calculate the volume of the region…

Q: Find the Volume enclosed by N = x2+y² and

A:

Q: Find the volume of the solid whose base is bounded by the circle x2 + y? = 36 and whose cross…

A: Given query is to find the volume of the give solid.

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

A:

Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

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…

A:

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: The volume of the closed cylindrical tank is 11.3 m 3 . If the total surface area is a minimum, what…

A: Given: Volume of cylindrical tank is 11.3m3.

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

A:

Q: find the volume aquired by taking by region bound by  y=x^2 and  y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1.…

Q: A company is constructing an open-top, square-based, rectangular metal tank that will have a volume…

A:

Q: Find the volume of the sdid of revolution below. (1,1) 05 y=x

A:

Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

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

A:

Q: Find the volume of the following tetrahedron: z)|0<x<2(1-z), 0<y<3| 1 T =

A: Given that  The region of the tetrahedron is  To fidn the volume of the tetrahedron is

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

A:

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: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

A:

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

A:

Q: use the washers method to find the volume (in units3) when the region bounded by curves y=x+2,…

A: In this question we will use basic of calculus i.e volume bounded by curves rotating about x axis.…

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.