The height of cylinder A is 6 cm and the height of cylinder B is h cm. The volume of cylinder A is 170 cm^3 and the volume of cylinder B is 573.75 cm^3. What is the value of h?
a)	4 cm
b)	9 cm
c)	12 cm
d)	20.25 cm
What type of problem is it? Fluency, understanding, reasoning or problem solving.


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**

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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.

The height of cylinder A is 6 cm and the height of cylinder B is h cm. The volume of cylinder A is 170 cm^3 and the volume of cylinder B is 573.75 cm^3. What is the value of h?
a) 4 cm
b) 9 cm
c) 12 cm
d) 20.25 cm

Solve for the height of cylinder B given its volume and compare it with cylinder A. This problem applies the volume formula for cylinders and algebraic manipulations, ideal for students in Grades 8-10. Learn how volume relates to height when the radius remains constant.

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