Question

The volume of a sphere is 1928π m3 . What is the surface area of the sphere to the nearest tenth?

Answer 1

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4}{3}\pi r^3\qquad \begin{cases} r=radius\\ ------\\ V=1928\pi \end{cases}\implies 1928\pi =\cfrac{4}{3}\pi r^3 \\\\\\ 1928\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3\cdot 1928\pi }{4\pi } =r^3\implies 1446=r^3 \\\\\\ \sqrt[3]{1446}=r\\\\ -------------------------------\\\\ \textit{surface area of a sphere}\\\\ S=4\pi r^2\qquad r=\sqrt[3]{1446}\implies S=4\cdot \pi \cdot \sqrt[3]{1446^2}$

Answer 2

Using the equation: A=pi^1/3(6(1928pim^3))^2/3 ; you should get the answer A= 749.13. Hopefully that helps