One Cylinder Has A Volume That Is $8 , \text{cm}^3$ Less Than 7 8 \frac{7}{8} 8 7 ​ Of The Volume Of A Second Cylinder. If The Volume Of The First Cylinder Is 216 Cm 3 216 \, \text{cm}^3 216 Cm 3 , What Is The Correct Equation And Value Of

Introduction

In this article, we will delve into a mathematical problem involving two cylinders with different volumes. We will explore the relationship between the volumes of these cylinders and derive an equation to represent this relationship. Our goal is to find the correct equation and value that describes the volume of the second cylinder.

Problem Statement

Let's consider two cylinders, Cylinder A and Cylinder B. The volume of Cylinder A is given as $216 \, \text{cm}^3$. Cylinder B's volume is $\frac{7}{8}$ of Cylinder A's volume, minus $8 \, \text{cm}^3$. We need to find the correct equation and value that represents the volume of Cylinder B.

Mathematical Representation

Let's denote the volume of Cylinder A as $V_A$ and the volume of Cylinder B as $V_B$. We are given that $V_A = 216 \, \text{cm}^3$. The volume of Cylinder B is $\frac{7}{8}$ of Cylinder A's volume, minus $8 \, \text{cm}^3$, which can be represented as:

$$V_B = \frac{7}{8}V_A - 8$$

Substituting the value of $V_A$, we get:

$$V_B = \frac{7}{8}(216) - 8$$

Simplifying the Equation

To simplify the equation, we can first calculate the value of $\frac{7}{8}(216)$:

$$\frac{7}{8}(216) = 189$$

Now, we can substitute this value back into the equation:

$$V_B = 189 - 8$$

Calculating the Volume of Cylinder B

To find the volume of Cylinder B, we can now subtract $8$ from $189$:

$$V_B = 181 \, \text{cm}^3$$

Conclusion

In this article, we explored a mathematical problem involving two cylinders with different volumes. We derived an equation to represent the relationship between the volumes of these cylinders and found the correct value that represents the volume of Cylinder B. The volume of Cylinder B is $181 \, \text{cm}^3$.

Key Takeaways

• The volume of Cylinder B is $\frac{7}{8}$ of Cylinder A's volume, minus $8 \, \text{cm}^3$.
• The correct equation to represent the volume of Cylinder B is $V_B = \frac{7}{8}V_A - 8$.
• The volume of Cylinder B is $181 \, \text{cm}^3$.

Further Exploration

This problem can be extended to explore other mathematical concepts, such as:

• Finding the ratio of the volumes of the two cylinders.
• Exploring the relationship between the radii and heights of the two cylinders.
• Generalizing the equation to represent the volume of Cylinder B in terms of the volume of Cylinder A.

Introduction

In our previous article, we explored a mathematical problem involving two cylinders with different volumes. We derived an equation to represent the relationship between the volumes of these cylinders and found the correct value that represents the volume of Cylinder B. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the relationship between the volumes of the two cylinders?

A: The volume of Cylinder B is $\frac{7}{8}$ of Cylinder A's volume, minus $8 \, \text{cm}^3$.

Q: How do we calculate the volume of Cylinder B?

A: To calculate the volume of Cylinder B, we can use the equation $V_B = \frac{7}{8}V_A - 8$, where $V_A$ is the volume of Cylinder A.

Q: What is the value of the volume of Cylinder B?

A: The volume of Cylinder B is $181 \, \text{cm}^3$.

Q: Can we find the ratio of the volumes of the two cylinders?

A: Yes, we can find the ratio of the volumes of the two cylinders by dividing the volume of Cylinder B by the volume of Cylinder A. The ratio is $\frac{181}{216}$.

Q: How do we simplify the equation $V_B = \frac{7}{8}V_A - 8$?

A: To simplify the equation, we can first calculate the value of $\frac{7}{8}(216)$, which is $189$. Then, we can substitute this value back into the equation to get $V_B = 189 - 8$.

Q: What is the significance of the value $8 \, \text{cm}^3$ in the equation?

A: The value $8 \, \text{cm}^3$ represents the difference in volume between the two cylinders.

Q: Can we generalize the equation to represent the volume of Cylinder B in terms of the volume of Cylinder A?

A: Yes, we can generalize the equation to represent the volume of Cylinder B in terms of the volume of Cylinder A. The general equation is $V_B = \frac{7}{8}V_A - k$, where $k$ is a constant.

Q: What is the value of the constant $k$ in the general equation?

A: The value of the constant $k$ is $8 \, \text{cm}^3$.

Conclusion

In this article, we answered some frequently asked questions related to the mathematical problem involving two cylinders with different volumes. We explored the relationship between the volumes of the two cylinders, calculated the volume of Cylinder B, and found the ratio of the volumes of the two cylinders. We also simplified the equation and generalized it to represent the volume of Cylinder B in terms of the volume of Cylinder A.

Key Takeaways

• The volume of Cylinder B is $\frac{7}{8}$ of Cylinder A's volume, minus $8 \, \text{cm}^3$.
• The correct equation to represent the volume of Cylinder B is $V_B = \frac{7}{8}V_A - 8$.
• The volume of Cylinder B is $181 \, \text{cm}^3$.
• The ratio of the volumes of the two cylinders is $\frac{181}{216}$.
• The value of the constant $k$ in the general equation is $8 \, \text{cm}^3$.

Further Exploration

This problem can be extended to explore other mathematical concepts, such as:

• Finding the relationship between the radii and heights of the two cylinders.
• Exploring the relationship between the volumes of the two cylinders and the surface area of the cylinders.
• Generalizing the equation to represent the volume of Cylinder B in terms of the volume of Cylinder A and other variables.