# Volume of 4 intersecting cylinders

• MHB
• Alex3535
In summary, I provided an expression for the volume of the left body, which is a cube with 4 smaller cubes attached to each corner, with a cylinder "cut" through each smaller cube. The expression is V = 4L^3 - πD^2L, where L is the side length of the cube and D is the diameter of the cylinder.
Alex3535
Hello.Can you please help me find an expression for the volume of the left body which is actually 4 cylinders with diameter = D placed on the vertices of the cube with side length L (the cylinders are being "cut" by the corners of the cube). Thank you!

#### Attachments

• 20180406_042255.jpg
32.9 KB · Views: 81

Hello there! Thank you for reaching out for help with your question. I am happy to assist you in finding an expression for the volume of the left body that you described.

To start, let's break down the problem into smaller parts. We have a cube with side length L and 4 cylinders with a diameter of D placed on the vertices of the cube. We can visualize this as a cube with 4 smaller cubes attached to each of its corners. Each of these smaller cubes will have a cylinder "cut" through its center, creating a hollow space inside.

To find the volume of the left body, we need to find the volume of each of these smaller cubes and subtract the volume of the cylinder that has been "cut" through it. Let's call the volume of the left body V, the volume of each smaller cube Vc, and the volume of the cylinder Vcy.

The volume of a cube is given by V = L^3, where L is the side length. Since we have 4 smaller cubes, the total volume of all 4 cubes would be 4Vc. Similarly, the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the radius would be half of the diameter, so r = D/2. The height of the cylinder would be the same as the side length of the cube, so h = L. Therefore, the total volume of all 4 cylinders would be 4Vcy.

To find the volume of the left body, we can use the following expression:

V = 4Vc - 4Vcy

Substituting the expressions for Vc and Vcy, we get:

V = 4(L^3) - 4(π(D/2)^2L)

Simplifying this further, we get:

V = 4L^3 - πD^2L

Therefore, the expression for the volume of the left body is:

V = 4L^3 - πD^2L

I hope this helps you in finding the volume of the left body in your problem. Let me know if you have any further questions. Best of luck!

## What is the formula for finding the volume of 4 intersecting cylinders?

The formula for finding the volume of 4 intersecting cylinders is V = πr²h, where r is the radius of the cylinders and h is the height of the intersection.

## How do you calculate the radius of a cylinder?

The radius of a cylinder can be calculated by dividing the diameter by 2. Alternatively, you can measure the distance from the center of the cylinder to the edge of the circular base.

## What is the significance of the height in the volume formula for 4 intersecting cylinders?

The height in the volume formula represents the length of the intersection between the cylinders. It is an important factor in calculating the total volume of the intersecting cylinders.

## Can the volume of 4 intersecting cylinders be negative?

No, the volume of 4 intersecting cylinders cannot be negative. Volume is a measure of space and cannot have a negative value.

## How can the volume of 4 intersecting cylinders be measured in real life?

The volume of 4 intersecting cylinders can be measured by filling the intersecting space with a known quantity of water and then measuring the volume of water using a graduated cylinder. This method is applicable in real life situations such as measuring the volume of a cylindrical container with objects inside.

### Similar threads

• General Math
Replies
8
Views
2K
• General Math
Replies
6
Views
2K
• Thermodynamics
Replies
5
Views
1K
• General Math
Replies
1
Views
4K
• General Math
Replies
1
Views
4K
• Thermodynamics
Replies
11
Views
2K
• General Math
Replies
2
Views
2K
• General Math
Replies
1
Views
4K
• Quantum Physics
Replies
1
Views
479
• General Math
Replies
4
Views
2K