Answer:
The volume of sphere is:
65.4167 yd^3
Step-by-step explanation:
We are given surface area of sphere as:
\(Area=25\pi\ \text{yd^2}\)
We know that the surface area of sphere of radius ''r'' is given by the formula:
\(Area=4\pi r^2\)
i.e. we have:
\(4\pi r^2=25\pi\\\\i.e.\\\\r^2=\dfrac{25}{4}\\\\\\r^2=(\ddfrac{5}{2})^2\\\\i.e.\\\\r=\pm \dfrac{5}{2}\)
As we know that the radius of a circle can't be negative.
Hence,
\(r=\dfrac{5}{2}\ \text{yd}\)
Now the volume of sphere is given by:
\(Volume=\dfrac{4}{3}\pi r^3\\\\i.e.\\\\Volume=\dfrac{4}{3}\pi (\dfrac{5}{2})^3\\\\i.e.\\\\Volume=65.4167\ \text{yd^3}\)
Volume of sphere is:
65.4167 yd^3
