2010年9月25日 · In summary, to express the volume of a cube as a function of the total surface area, we can manipulate the surface area equation to find the volume. Using the surface area equation of 6x^2 and the volume equation of x^3, we can substitute for x and solve for volume, resulting in the equation V = (S/6)^{3/2} or V = S^{3/2}/6^{3/2}.

2010年9月28日 · Surface area is greater by 11.48. Or if I go by your recommendation: 14.65 (The Total SA of 100 Droplets) / 3.14 (SA of the Original Surface Area) = 4.67 or 4.7. Total Surface Area of the 100 droplets is 4.7 times larger. What units can use to express surface area and volume given that the original droplet had a 1 centimeter diameter.

2013年3月7日 · Wrap a cylinder around that sphere. i.e. x^2+y^2 = R^2 with z between -R and R. Any region on the sphere has the same area as the corresponding area on the cylinder. The correspondence is via a radial projection out from the z axis. So, for example, the area between latitudes would be 2pi*R^2(cos(phi1)-cos(phi2)).

2009年8月24日 · Homework Statement Given that a solid cylinder has a fixed volume V, prove that its total surface area S is minimum when its height and base diameter are equal. Homework Equations derivative The Attempt at a Solution I am able to prove that question. V=\\pi r^2 h...

2012年8月29日 · What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 1.1 m on an edge? 2. The attempt at a solution 1) First, find the surface area of the cube: A = 6s² = 6 * (1.1 m)² = 7.26 m² 2) Next, find the surface area of one sand grain:

2011年11月1日 · The total surface area of a right circular cylinder is given by the formula A = 2pir(r + h) where r is the radius and h is the height. a) Find the rate of change of A with respect to h if r remains constant. b) Find the rate of change of A with respect to r if h remains constant. c) Find the rate of change of h with respect to r if A remains ...

2009年9月4日 · In summary, we need to use the equation for surface area of a sphere, A = 4πr^2, and the equation for volume, V = (4/3)πr^3. We also need to use the equation for mass, M = Vρ, where ρ is the density. After plugging in the given values, we find that the mass of sand grains with a total surface area equal to a 1.0 m cube is approximately 0.25 kg.

2011年2月19日 · Calculate the surface area of 1g of powder with a size of 100micrometer. Assume the particles are spherical. Then estimate the percentage of TiO2 molecules at the surface of the particle (relative to the total number of TiO2 molecules in the volume of the particle) for the same size. Assume the thickness of surface TiO2 is the diameter of O-2 ...

2007年2月3日 · What is the surface area and volume of a pressure vessel in the form of a cylinder with each end in the form of a hemisphere, if the overall length is 12 meters and the diameter is 3 meters. solution: given: radius = 1.5m diameter = 3m height or length = 12m pi=3.14-----Total surface area of a cylinder = 2*pi*r*h + 2*pi*r^2 TSA = 2*3.14*1.5*12 ...

2008年8月27日 · Find the dimensions of a rectangular box with the largest volume with surface area 64cm^2. Homework Equations area of a rectangular prism 2xy+2yz+2xz The Attempt at a Solution took 2xy+2yz+2xz=64 rearranging for z: z=(xy-32)/(y+x) partial derivative of z with respect to x y/(y+x)-(xy-32)/(y+x)^2 partial derivative of z with respect to y