Question

The volume of a sphere is 1476 pi m^3. what is the surface area of the sphere to the nearest tenth?

Answer 1

`\text{The formula of a volume of a sphere with radius R:}\\\\V=(4)/(3)\pi R^3\\\\\text{The formula of a surface area of the sphere with radius R:}\\\\A=4\pi R^2\\\\\text{We have}\ V=1476\ip\ m^3.\ \text{Substitute:}\\\\(4)/(3)\pi R^3=1476\pi\ \ \ \ |:\pi\\\\(4)/(3)R^3=1476\ \ \ \ |\cdot3\\\\4R^3=4428\ \ \ \ |:4\\\\R^3=1107\to R=\sqrt[3]{1107}\\\\R=\sqrt[3]{27\cdot41}\\\\R=\sqrt[3]{27}\cdot\sqrt[3]{41}\\\\R=3\sqrt[3]{41}`

`\text{Substitute the value of R to the formula of the surface area:}\\\\A=4\pi\cdot\left(3\sqrt[3]{41}\right)^2=4\pi\cdot9\sqrt[3]{41^2}=36\pi\sqrt[3]{1681}\approx1344.8\ m^2`