Find the volume of a sphere with surface area equal to 100π ft^2

Surface area of sphere = [tex]4 \pi r^{2} [/tex]

Volume of sphere = [tex] \frac{4}{3} \pi r^{3} [/tex]

[tex]100 \pi =4 \pi r^{2} [/tex]

Therefore [tex]r = 5[/tex]

Volume = [tex] \frac{4}{3} \pi *5^{3} = \frac{500 \pi }{3} [/tex]

Answer Link

jhonjez jhonjez · Answer 2 · 2019-07-27T00:56:57+02:00

Answer:

[tex]V=\frac{500}{3}\ \pi(ft^{3})[/tex]

Step-by-step explanation:

Hello.

to find the volume of a sphere we must know its radius,

we don't know the radius but we have the area

[tex]A=4\pi r^{2} \\ \\isolating\ r\\\\A=4\pi r^{2}\\r=\sqrt{\frac{A}{4\pi } } \\r=\sqrt{\frac{100\ ft^{2} }{4\pi}} \\\\ r= \sqrt{25\ ft^{2} }\\ r=5\ ft\\[/tex]

Now, replacing this value in the volume equation

[tex]V=\frac{4\pi r^{3} }{3} \\V=\frac{4\pi\ (5\ ft)^{3} }{3}\\ V=\frac{4\pi\ (125 ft^{3}) }{3}\\V=\frac{500}{3}\ \pi (ft^{3})\\\\\\[/tex]

have a great day