Question

part b
alex knows that his cone has a volume, v, of 150 cubic inches and a height, h, of 6 inches. he shows his steps to find the radius of the base, r, of the cone.
step 1: $v=\frac{1}{3}pi r^{2}h$
step 2: $\frac{v}{3pi h}=r^{2}$
step 3: $sqrt{\frac{v}{3pi r}} = r$
step 4: $sqrt{\frac{150}{3pi(6)}}=r$
step 5: $rapprox1.63$ inches
which statement about alexs work is true?
○a alex made an error from step 1 to step 2.
○b alex made an error from step 2 to step 3.
○c alex made an error from step 3 to step 4.
○d alex did not make any errors and correctly found the radius of the base of the cone.

Explanation:

Step1: Start with volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step2: Isolate $r^{2}$

Dividing both sides of $V = \frac{1}{3}\pi r^{2}h$ by $\frac{1}{3}\pi h$ gives $\frac{V}{\frac{1}{3}\pi h}=r^{2}$, which simplifies to $\frac{3V}{\pi h}=r^{2}$. Alex made an error here as in his Step 2 he wrote $\frac{V}{3\pi h}=r^{2}$ instead of $\frac{3V}{\pi h}=r^{2}$.

Step3: Analyze error location

Since the error is in the transition from Step 1 to Step 2.

Answer:

A. Alex made an error from Step 1 to Step 2.