A cylindrical can of height h and radius r is to be made with a fixed volume V. Show that the area of material used is minimised when h = 2r.

Q: A liquid with a relative density of 2 fully fills a conical reservoir with a top radius of 3' and a…

A: A liquid with a relative density of 2 fully fills a conical reservoir with a top radius of 3' and a…

Q: The 0.50 lb ball is shot from the spring device shown. The spring has a stiffness k = 10 lb/in. and…

A: Image is attached with detailed solution.

Q: 3. A hemispherical tank of radius 10 ft is filled with a liquid of density p to a depth of 6 ft. as…

A:

Q: The dimensions of the control volume of the figure are L = 20 in, H = 15.4 in, W = 13.0 in and the…

A:

Q: 2. In this problem we prove that if Au(x, y) bounded function then u must be a constant. Hence if u…

A: Suppose that ∆ux,y=0, for all x,y. Given that u is bounded, that is, ux, y≤M, for all x,y. Let vx,…

Q: 2. How much work is required to pump all the water out of a cylindrical tank with a height of 10m…

A:

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: 2) The radius of a sphere decreases at the rate of 2 m/sec. Find the rate at which the volume…

A:

Q: The boundary of a lamina consists of the semicircles y=√16-x² and y= √36-x2 together with the…

A: Here we have to find the centre of the mass of the lamina.

Q: 0. 50 TT+4 7.) A cylindrical can, with lid, must hold 2 liters of liquid (2000 cm'). Find the height…

A: Let height = h and radius of the base = r. Then, volume V = πr2h = 2000 cc    .........[1]and…

Q: 1. A hemispherical bowl of radius 10 m is filled with water. There is a small hole of radius 10 cm…

A:

Q: 3. The boundary of a lamina consists of the semicircles y = √√√1 - x² and y = √√4x² together with…

A:

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: