# Related Rates cylinder problem

• Mitchtwitchita
In summary, a "Related Rates cylinder problem" is a type of calculus problem that involves finding the rate of change of one variable with respect to another, specifically the volume or surface area of a cylinder. The approach to solving these problems involves identifying given information, using formulas, taking derivatives, and plugging in values. Common mistakes to avoid include not correctly identifying information, using incorrect formulas, and not simplifying the equation. Helpful tips include drawing diagrams and labeling variables, and the most efficient method is typically using calculus.
Mitchtwitchita
A cylinder is placed in oven where both the height and base radius expand at 0.1 mm/min. When the height is 250 mm and the radius of the base 30 mm, the volume is expanding at ...mm3 /min. (Answer to nearest whole number)

r=30, h=250, dr/dh=0.1, dh/dt=0.1

dV/dt = (pi)r^2(dh/dt) + 2rh(dr/dt)
=(pi(30)^2(0.1) + 2(30)(250)(0.1)
=1783

Can anybody please show me where I'm going wrong with this one?

$$V=\pi r^2h$$

You're missing a pi term!

$$\frac{dV}{dt}=\pi[2hr\frac{dr}{dt}+r^2\frac{dh}{dt}]$$

Thanks roco!

## 1. What is a "Related Rates cylinder problem"?

A "Related Rates cylinder problem" is a type of calculus problem that involves finding the rate of change of one variable with respect to another, in this case, the rate of change of the volume or surface area of a cylinder. This type of problem is often used in real-world applications, such as calculating the rate at which water is filling a cylindrical tank or the rate at which a balloon is deflating.

## 2. How do I approach solving a "Related Rates cylinder problem"?

The first step in solving a "Related Rates cylinder problem" is to identify the given information and the desired rate of change. Then, use the given formulas for the volume and surface area of a cylinder to create an equation that relates the variables. Next, take the derivative of both sides of the equation with respect to time. Finally, plug in the given values and solve for the desired rate of change.

## 3. What are some common mistakes to avoid when solving a "Related Rates cylinder problem"?

Some common mistakes to avoid when solving a "Related Rates cylinder problem" include not correctly identifying the given information and the desired rate of change, not using the correct formulas for volume and surface area, and not taking the derivative correctly. It is also important to pay attention to units when plugging in values and to simplify the equation as much as possible before solving for the desired rate of change.

## 4. Are there any tips or tricks for solving "Related Rates cylinder problems"?

One helpful tip for solving "Related Rates cylinder problems" is to draw a diagram of the situation and label all given values and variables. This can help you visualize the problem and identify any missing information. Additionally, it can be helpful to write out the given formula for volume or surface area and label each variable with its corresponding rate of change.

## 5. Can "Related Rates cylinder problems" be solved using any other methods?

While the traditional approach to solving "Related Rates cylinder problems" involves using calculus, there are also other methods that can be used. For example, some problems may be solved using geometric reasoning or by setting up a proportion. However, the calculus method is generally the most efficient and accurate way to solve these types of problems.

• Calculus and Beyond Homework Help
Replies
11
Views
599
• Calculus and Beyond Homework Help
Replies
24
Views
990
• Calculus
Replies
2
Views
2K
• Calculus
Replies
2
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
822
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
13
Views
1K
• Classical Physics
Replies
1
Views
794
• Special and General Relativity
Replies
8
Views
1K
• General Math
Replies
1
Views
5K