Question

What is the volume of a sphere with the surface area of 25 pi yd^2 ?

Answer 1

Answer:

$V=65.4 yd^{3}$

Step-by-step explanation:

To be able to calculate the sphere's volume, we have to know first what is the sphere's radius. The formula to calculate said volume is:

$V=\frac{4}{3}. \pi . r$

And the sphere's surface area formula is:

$SA=4. \pi . r^{2}$

If we know that the value of the area is $25 pi . yd^{2}$ we can sustitute:

$25 pi . yd^{2}=4. \pi . r^{2}$

Now we can isolate the radius of the sphere.

$\frac{25 pi . yd^{2}}{4. \pi }= r^{2}$

$\sqrt{\frac{25 pi . yd^{2}}{4. \pi }}=r$

$\sqrt{\frac{25 pi . yd^{2}}{4. \pi }}=r$

$\sqrt{6.25 yd^{2}}=r$

$2,5 yd =r$

Now that we know the radius we can sustitute it's value on the volume formula, and the result is the volume of the sphere!

$V=\frac{4}{3}. \pi . (2,5 yd)^{3}$

$V=\frac{4}{3}. \pi . 15.625 yd^{3}$

$V=65.4 yd^{3}$