Question

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

Answer 1

Answer:

$V=\frac{500}{3}\ \pi(ft^{3})$

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

$A=4\pi r^{2} \\ \\isolating\ r\\\\A=4\pi r^{2}\\r=\sqrt{\frac{A}{4\pi } } \\r=\sqrt{\frac{100\ ft^{2} }{4\pi}} \\\\ r= \sqrt{25\ ft^{2} }\\ r=5\ ft$

Now, replacing this value in the volume equation

$V=\frac{4\pi r^{3} }{3} \\V=\frac{4\pi\ (5\ ft)^{3} }{3}\\ V=\frac{4\pi\ (125 ft^{3}) }{3}\\V=\frac{500}{3}\ \pi (ft^{3})$

have a great day

Answer 2

Surface area of sphere = $4 \pi r^{2}$

Volume of sphere = $\frac{4}{3} \pi r^{3}$

$100 \pi =4 \pi r^{2}$

Therefore $r = 5$


Volume = $\frac{4}{3} \pi *5^{3} = \frac{500 \pi }{3}$