Question

Not to be outdone, Austin of delectable wants to double the volume of the jawbreaker that Karen made (1150.4in^3) What is the jawbreakers diameter?

Answer 1

The volume of a sphere is given by the following formula:

`V=(4)/(3)((d)/(2))^3\pi`

We can use this formula to write the diameter as a function of the volume.

`d=^{}2((3)/(4\pi)V)^{(1)/(3)}`

We know the volume for Karen's Jawbreaker, it is 1150.4 in^3. Austen wants to double it

`2(1150.4)=2300.8`

Since we know the desired volume, we can just evaluate this volume in our formula

`d=2((3)/(4\pi)2300.8)^{(1)/(3)}=16.3792275136\approx16.38in`

With this, we have our diameter. 16.38 inches.