Respuesta :

[tex] \bf \textit{surface area of a sphere}\\\\
SA=4\pi r^2\qquad \qquad \implies \stackrel{SA}{400\pi }=4\pi r^2\implies \cfrac{400\pi }{4\pi }=r^2
\\\\\\
100=r^2\implies \sqrt{100}=r\implies \boxed{10=r}
\\\\\\
\textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\qquad \qquad V=\cfrac{4\pi \boxed{10^3}}{3}\implies V=\cfrac{4000\pi }{3} [/tex]

JeanaShupp

Answer: [tex]1333.33\pi\ ft.^3[/tex]

Step-by-step explanation:

The surface area of sphere is given by :-

[tex]S.A=4\pi r^2[/tex], where r is radius of sphere.

Given : Surface area of sphere =[tex] 400 \pi \ft2[/tex]

[tex]\\\Rightarrow 400 \pi =4\pi r^2\\\\\Rightarrow\ r^2=\dfrac{400}{4}=100\text{ ft.}[/tex]

The volume of sphere is given by :-

[tex]V=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ V=\dfrac{4}{3}\pi (100)^3\\\\\Rightarrow\ V=\dfrac{4000}{3}\pi=1333.33333\approx1333.33\pi\ ft.^3[/tex]

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