Question

monte performs an experiment using 2 identical graduated cylinders, each with a radius of 2 centimeters.the volume of the liquid in the first graduated cylinder is 188.4 cubic centimeters. the volume of the liquid in the second graduated cylinder is 314 cubic centimeters.what is the difference in the height of the liquid in the two cylinders?use 3.14 for pi.enter your answer in the box.

Explanation:

Step1: Recall cylinder volume formula

The volume of a cylinder is $V = \pi r^2 h$, so we rearrange to solve for height: $h = \frac{V}{\pi r^2}$

Step2: Calculate height of first cylinder

Substitute $V_1=188.4$, $\pi=3.14$, $r=2$:
$h_1 = \frac{188.4}{3.14 \times 2^2} = \frac{188.4}{3.14 \times 4} = \frac{188.4}{12.56} = 15$ cm

Step3: Calculate height of second cylinder

Substitute $V_2=314$, $\pi=3.14$, $r=2$:
$h_2 = \frac{314}{3.14 \times 2^2} = \frac{314}{3.14 \times 4} = \frac{314}{12.56} = 25$ cm

Step4: Find height difference

Subtract the two heights: $h_2 - h_1 = 25 - 15$

Answer:

10 centimeters