Question

What is the volume of a sphere that with a great circle that has an area of 225(pi) square centimeters?

Answer 1

Answer on Question #42316 – Math – Geometry

Question. What is the volume of a sphere that with a great circle that has an area of $225\pi$ square centimeters?

Solution. Notice that the radius of a sphere is equal to the radius of its great circle. Also recall that the volume of a sphere of radius $r$ is given by the formula:

$V=\frac{4}{3}\,\pi r^{3},$

while the area of a circle of the same radius $r$ is

$A=\pi r^{2}.$

In our case

$A=\pi r^{2}=225\,\pi,$

whence $r^{2}=225$ and so

$r=\sqrt{225}=15\ cm.$

Therefore the volume of the sphere is equal to

$V=\frac{4}{3}\,\pi r^{3}=\frac{4}{3}\,\pi\cdot 15^{3}=4\cdot 15^{2}\cdot 5\pi=20\cdot 225\pi=4500\ cm^{3}.$

Answer. $V=4500\ cm^{3}.$