Answer:
[tex]r_c=\sqrt{\frac{A}{2\pi}} \ units[/tex]
[tex]r_d=\frac{3}{2}\sqrt{\frac{A}{\pi}} \ units[/tex]
Step-by-step explanation:
we have
The surface area of sphere B is A square units ---> [tex]S_B=A\ units^2[/tex]
The surface area of sphere C is twice that of sphere B __> [tex]S_C=2A\ units^2[/tex]
The surface area of sphere D is nine times that of sphere B
[tex]S_D=9A\ units^2[/tex]
Remember that
The surface area of a sphere is equal to
[tex]S=4\pi r^{2}[/tex]
step 1
Find the radius of sphere C
[tex]S_C=2A\ units^2[/tex]
so
[tex]4\pi(r_c)^2=2A[/tex]
Solve for r_c
[tex]r_c=\sqrt{\frac{2A}{4\pi}} \ units[/tex]
Simplify
[tex]r_c=\sqrt{\frac{A}{2\pi}} \ units[/tex]
step 2
Find the radius of sphere D
[tex]S_D=9A\ units^2[/tex]
so
[tex]4\pi(r_d)^2=9A[/tex]
Solve for r_d
[tex]r_d=\sqrt{\frac{9A}{4\pi}} \ units[/tex]
simplify
[tex]r_d=\frac{3}{2}\sqrt{\frac{A}{\pi}} \ units[/tex]
