The volume of a sphere is given by the following formula:
[tex]V=\frac{4}{3}(\frac{d}{2})^3\pi[/tex]We can use this formula to write the diameter as a function of the volume.
[tex]d=^{}2(\frac{3}{4\pi}V)^{\frac{1}{3}}[/tex]We know the volume for Karen's Jawbreaker, it is 1150.4 in^3. Austen wants to double it
[tex]2(1150.4)=2300.8[/tex]Since we know the desired volume, we can just evaluate this volume in our formula
[tex]d=2(\frac{3}{4\pi}2300.8)^{\frac{1}{3}}=16.3792275136\approx16.38in[/tex]With this, we have our diameter. 16.38 inches.