- #1

- 5

- 0

We will define a cone in n-dimensions as a figure with a cross - section along its height [tex]X_n [/tex] that has a constant shape, but each of its dimensions is shrunk linearly to 0.

a)let D be a cone in [tex] R^n [/tex] with height h [tex] (ie. [/tex] [tex] X_n [/tex] [tex] \epsilon [/tex] [tex] [0, h]) [/tex] and let the volume of its cross-section at h=0 be [tex] V_o [/tex]. Find the volume of D in terms of [tex]V_o [/tex].

b)Find the volume of the region defined by [tex]|x_1| +...+ |x_n| \le r [/tex] in [tex] R^n [/tex], using a)