This problem involves comparing the volumes and heights of two cylinders. We need to find the height $h$ of cylinder B, given its volume and the known volume and height of cylinder A. Here's the step-by-step solution:

Step 1: Recall the formula for the volume of a cylinder

The volume $V$ of a cylinder is given by: $V = \pi r^2 h$ where $r$ is the radius of the cylinder and $h$ is its height.

Step 2: Relate the volumes of cylinders A and B

Let $r$ be the radius of both cylinders since it is not specified that the radii differ. We have:

• Volume of cylinder A, $V_A = 170 \text{ cm}^3$
• Height of cylinder A, $h_A = 6 \text{ cm}$

So, $170 = \pi r^2 \cdot 6$ Solving for $r^2$, we get: $r^2 = \frac{170}{6\pi}$

Step 3: Use the radius to find the height of cylinder B

The volume of cylinder B is given as $573.75 \text{ cm}^3$: $573.75 = \pi r^2 \cdot h$ Substitute $r^2 = \frac{170}{6\pi}$: $573.75 = \pi \left(\frac{170}{6\pi}\right) \cdot h$ Simplifying: $573.75 = \frac{170}{6} \cdot h$ $h = \frac{573.75 \cdot 6}{170} = 20.25 \text{ cm}$

Thus, the height of cylinder B is $h = 20.25 \text{ cm}$.

Problem Type

This problem is primarily an example of problem-solving since it involves applying known formulas, performing algebraic manipulations, and logical reasoning to find the answer.

Answer

The correct answer is: d) 20.25 cm

---

Would you like more details or have any other questions?

Related Questions

1. How would the answer change if the radius of cylinder B was different from cylinder A?
2. What is the relationship between the volumes of cylinders with the same radius but different heights?
3. Can you find the radius of cylinder A given the information above?
4. How does changing the height affect the volume of a cylinder if the radius remains constant?
5. What are the implications for surface area when the height of a cylinder changes?

Tip

Always remember to check if other variables (like radius in this case) remain constant when comparing geometric figures. This simplifies calculations significantly.