To solve this problem, let's break down the options given and explain why the correct one involves dividing the product of 12 and 9 by 3.
1. Isabella should have divided 12 by 2 before squaring to get [tex]\( V = \frac{1}{3}(B)^2(9) \pi \)[/tex]:
- This option does not align with our problem since we are working with the numbers 12 and 9 directly and not with some intermediate division and squaring steps.
2. Isabella should have squared 9 instead of 12 to get [tex]\( V = \frac{1}{3}(9)^2(12) \pi \)[/tex]:
- Squaring 9 or 12 is not mentioned in the context of our original problem.
3. Isabella should have divided the product of 12 and 9 by 3 to get [tex]\( V = \frac{12(9)}{3} \)[/tex]:
- This aligns with the correct approach. To find the correct volume [tex]\( V \)[/tex], Isabella should multiply 12 and 9 first to get 108, and then divide by 3, resulting in 36.
4. Isabella should have divided the product of [tex]\( 12 \pi \)[/tex] and 9 by 3 to get [tex]\( V = \frac{12 \pi(9)}{3} \)[/tex]:
- This option unnecessarily complicates the formula as [tex]\(\pi\)[/tex] is not part of our original needs for 12 and 9.
Given this, the correct step-by-step solution to identify Isabella's error is:
1. Calculate the product of 12 and 9:
[tex]\[
12 \times 9 = 108
\][/tex]
2. Divide the product by 3:
[tex]\[
\frac{108}{3} = 36
\][/tex]
Therefore, the correct statement is:
- Isabella should have divided the product of 12 and 9 by 3 to get [tex]\( V = \frac{12(9)}{3} \)[/tex].
By doing so, Isabella would obtain the correct volume as 36.
