Please use Archimedes’ approach not” modern” formulas
a) Prove that the volume of a sphere is equal to 4 of its corresponding cones
b) Prove that the surface area of a sphere is equal to 4 of its corresponding great circles.
Please use Archimedes’ approach not” modern” formulas a) Prove that the volume of a sphere is...
5. Use the approach of Cavalieri to prove the formula of Archimedes for the volume of the sphere: show that the area of the section of the sphere 2,2 +y2 +za_ r2 by the plane y = c,-1 c 1, is equal to the area of the section of the cylinder 22 outside of the cone2+222 and use the formula for the volume of the cone.
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4, Rʻ,...). Notation & Terminology: Use V, and S, for the "volume" and "surface area" of an n- dimensional solid sphere. Thus "Volume" is not always in cubic units, it is in units^n. So, similarly “surface area" is in units (n-1) and is the measurement of the boundary. 1. Look up & become familiar with the formulas for V, and S. Start in R', what...
Prove that the surface area of a sphere is V = 4*pi*a^2 using parametric equations. Then re-prove it using polar equations. Only use one integral for polar please.
Write a program to calculate the volume and surface area of a sphere from it radius given as input. Here are some formulas that might be useful: V = 4/3πr3 A = 4 πr2
Calculus 1 work only please!
Parabolic Arch Archimedes showed that the area of a parabolic arch is equal to į the product of the base and the height (see figure). h b (a) Graph the parabolic arch bounded by y = 9 – x2 and the x-axis. Use an appropriate integral to find the area A. (b) Find the base and height of the arch and verify Archimedes' formula.
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
Please answer all three parts. Please write down formulas that
you use and write down explanations when needed! Will give you
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4. (a) let x[n] be a finite duration signal of duration N. Let y[n] = DFT(DFT(a[n])). All DFTs are N point DFTs. Find vinl in termas of rinl Prove all the properties you use in arriving at your result (b) Let an] and yIn] be sequences of duration N with...
A sphere of radius r has surface area A = 4πr2 and volume V = (4/3) πr3. The radius of sphere 2 is double the radius of sphere 1. (a)What is the ratio of the areas, A2/A1? (b)What is the ratio of the volumes, V2/V1?
can you please answer b
with formulas end explaination
I. A solid, non-conducting sphere of radius a carries a charge of +6 μC. This sphere is located at the center of a hollow, conducting sphere with an inner radius of b and an outer radius of c as shown. The hollow sphere also carries a total excess charge of +6 HC. d) y ouer Surface: 666e12/Mc (2 (a) Determine (i) the charge on the inner surface of the outer sphere...
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q Concentric with this sphere is a conducting, hollow sphere with total charge -Q, whose inner and outer radii are b and c as shown in the figure. Express all your answers in terms of Q, a, b, c,r and k, or o as appropriate (a) [4 pts.] Draw an appropriate Gaussian surface and use it to find the electric field...