Answer: [tex]14.13\text{ yd}^3[/tex]
Step-by-step explanation:
The surface area of a sphere is given by :-
[tex]S.A.=4\pi r^2[/tex], where r is the radius of the sphere.
Given : Surface Area of sphere=[tex]9\pi\ \text{yd}^2[/tex]
By the above formula , we have
[tex]9\pi=4\pi r^2\\\\\Rightarrow\ r^2=\dfrac{9}{4}\\\\\Rightarrow\ r=\dfrac{3}{2}=1.5\text{ yd}[/tex]
The volume of sphere is given by :-
[tex]V=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ V=\dfrac{4}{3}(3.14)(1.5)^3=14.13\text{ yd}^3[/tex]
Hence, the volume of sphere = [tex]14.13\text{ yd}^3[/tex]
