Mathematics, 17.07.2019 02:30 alyssamiller401
The volume of a sphere is 1476 pi m^3. what is the surface area of the sphere to the nearest tenth?
Answers: 1
![\text{The formula of a volume of a sphere with radius R:}\\\\V=\dfrac{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:}\\\\\dfrac{4}{3}\pi R^3=1476\pi\ \ \ \ |:\pi\\\\\dfrac{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}](/tpl/images/0098/5019/aa67a.png)
![\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](/tpl/images/0098/5019/f6d0c.png)
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The volume of a sphere is 1476 pi m^3. what is the surface area of the sphere to the nearest tenth?...
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