Question

Drag the points to create two different cylinders with the

same volume.
What is the volume of one cylinder

Answer 1

By adjusting dimensions while keeping the product of radius and height constant, two cylinders with equal volumes can be created. The example illustrates this principle with volumes of 45π.

To achieve two different cylinders with the same volume, we can manipulate the dimensions while keeping the product of the radius and height constant. The volume (V) of a cylinder is calculated using the formula:

Volume = π * r^2 * h

In the given scenario, the volume of one cylinder is 45π. To create two cylinders with the same volume, we can vary the dimensions. Let's consider two cylinders:

Cylinder 1:

Volume_1 = π * r_1^2 * h_1

Cylinder 2:

Volume_2 = π * r_2^2 * h_2

To maintain equal volumes, we need to satisfy the condition Volume_1 = Volume_2, implying:

π * r_1^2 * h_1 = π * r_2^2 * h_2

Given that the volume of one cylinder is 45π, we can choose specific values for r_1, h_1, r_2, and h_2. For instance:

Cylinder 1: r_1 = 3, h_1 = 5

Volume_1 = π * (3)^2 * 5 = 45π

Cylinder 2: r_2 = 6, h_2 = 4

Volume_2 = π * (6)^2 * 4 = 45π

The volume of one cylinder is 45π, and by adjusting the dimensions, we can create two cylinders with equal volumes.

Answer 2

To create two different cylinders with the same volume the volume of one cylinder is 45π.

The volume of a cylinder is calculated with the formula:

Volume =
`pi * radius^2 * height`

Therefore, to create two different cylinders with the same volume, we need to keep the product of the radius and the height the same. We can do this by increasing the radius and decreasing the height, or vice versa.

In the image you have provided, the two cylinders have the following dimensions:

Cylinder 1: radius = 3, height = 5

Cylinder 2: radius = 6, height = 4

To calculate the volume of each cylinder, we can use the formula above:

`Volume of Cylinder 1 = pi * 3^2 * 5 = 45pi`

`Volume of Cylinder 2 = pi * 6^2 * 4 = 144pi`

As you can see, the volumes of the two cylinders are equal, even though they have different dimensions.

Answer: The volume of one cylinder is 45pi.

Step-by-step explanation:

The two cylinders have different dimensions, but they have the same volume because the product of their radii and heights is the same.