a) Show that the astroidal sphere

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a) Show that the astroidal sphere

a) Show that the astroidal sphere $x^{\frac{2}{3}}+y^{\frac{2}{3}}+z^{\frac{2}{3}}=a^{\frac{2}{3}}$ can be represented parametrically as $x=a(\sin (u) \cos (v))^{3}, y=a(\sin (u) \sin (v))^{3}, z=a(\cos (u))^{3},(0 \leq u \leq \pi, 0 \leq v \leq 2 \pi)$

b) Find the volume of astroiadal sphere using a triple integral and the transformations $x=\rho(\sin \varphi \cos \theta)^{3}, y=\rho(\sin \varphi \sin \theta)^{3}, \rho(\cos \varphi)^{3}$ for which $0 \leq \rho \leq a, 0 \leq \phi \leq \pi, 0 \leq \theta \leq 2 \pi$

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a) Show that the astroidal sphere

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