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Lemur [1.5K]
3 years ago
15

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

Mathematics
1 answer:
ratelena [41]3 years ago
5 0

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}

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