the sunshine orange juice company wants its product in a one quart container(1 quart=107.75 cubic inches). the manufacturer for their containers makes cylindrical cans that have a base that is 5 inches in diameter. what will be the height of the one quart container?

V=πr^2h

107.75 = 3.12 * 2.5^2 * h

107.75 = 19.625h

107.75/19.625 = h

5.49 = h

To find the height of the one-quart container, we need to calculate the volume of the container and then solve for the height.

The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
Where:
π is a mathematical constant approximately equal to 3.14
r is the radius of the base (half the diameter)
h is the height of the cylinder

Given that the base diameter is 5 inches, the radius (r) would be half of that, which is 5/2 = 2.5 inches.

Now, let's plug these values into the volume formula:
107.75 cubic inches = π * (2.5 inches)^2 * h

Simplifying further, we get:
107.75 = 3.14 * 6.25 * h
107.75 = 19.625 * h

To solve for h, divide both sides of the equation by 19.625:
107.75 / 19.625 = h

The height of the one-quart container is:
h ≈ 5.5 inches

To find the height of the one quart container, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Where:
- Volume is the total volume of the container (107.75 cubic inches in this case)
- π is a mathematical constant, approximately equal to 3.14159
- r is the radius of the base of the container (which is half of the diameter)
- h is the height of the container

Given that the base diameter is 5 inches, we can calculate the radius as follows:

Radius (r) = Diameter / 2 = 5 inches / 2 = 2.5 inches

Now, we can substitute the values into the formula and solve for the height:

107.75 = π * (2.5)^2 * h

First, let's calculate the value of (2.5)^2:

(2.5)^2 = 2.5 * 2.5 = 6.25

Now, we can rearrange the formula and solve for h:

107.75 = 3.14159 * 6.25 * h

Divide both sides by (3.14159 * 6.25) to isolate h:

h = 107.75 / (3.14159 * 6.25)

Calculating this, the height of the one quart container comes out to be approximately 3.44 inches. Therefore, the height of the one quart container will be approximately 3.44 inches.