Chapter 7 - Exponents and Exponential Functions - 7-2 Multiplying Powers With the Same Base - Practice and Problem-Solving Exercises - Page 431: 58

a. $A=4r^{2}$ b. $64$ sq.in. c. $14$ in.

$a.$ The side length of the box is two radii, $2r.$ The area of a square with side length $2r$ is $A=(2r)^{2}=2^{2}r^{2}=4r^{2}$ $b.$ If $r=4$ in, $A=4\cdot 4^{2}=4\cdot 16=64$ sq.in. $c.$ If $A=196,$ then $4r^{2}=196$ $r^{2}=49$ $r=9$ So, the greatest diameter is $2r=14$ in.