a right circular cylindrical container ,contains 2160cubic cm water. if the diameter of the base of the cylindrical container is 24 cm, then find the height of the cylindrical container.

V = A ∙ h

V = Volume of a circular cylinder

A = Area of a base

h = height

In this case:

A = d²∙ π / 4

so:

V = A ∙ h

V = ( d²∙π / 4 ) ∙ h

V = 2160 cm³

d = 24 cm

2160 = ( 24²∙ π / 4 ) ∙ h

2160 = ( 576 ∙ π / 4 ) ∙ h

2160 = 576 π ∙ h / 4

Multiply both sides by 4

2160 ∙ 4 = 576 π ∙ h

8640 = 576 π ∙ h

Divide both sides by 576 π

8640 / ( 576 π ) = h

576 ∙ 15 / ( 576 π ) = h

15 / π = h

h = 15 / π

h = 15 / 3.141592654

h = 4.774648292 cm

h = 15 / π cm

h ≈ 4.775 cm

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

Volume = π * r^2 * h

Given that the diameter of the base of the cylindrical container is 24 cm, we can find the radius by dividing the diameter by 2:

Radius = 24 cm / 2 = 12 cm

Substituting the known values into the volume formula, we have:

2160 cm^3 = π * 12^2 * h

Simplifying, we get:

2160 cm^3 = 144π cm^2 * h

To isolate h, we divide both sides of the equation by 144π cm^2:

h = 2160 cm^3 / (144π cm^2)

Using the approximate value of π as 3.14, we can calculate the height:

h = 2160 cm^3 / (144 * 3.14 cm^2)
h ≈ 4.7 cm

Therefore, the height of the cylindrical container is approximately 4.7 cm.

To find the height of the cylindrical container, you need to use the formula for the volume of a cylinder.

The formula for the volume of a cylinder is given by:

V = π * r^2 * h

where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the diameter of the base of the cylindrical container is 24 cm, we can find the radius (r) by dividing the diameter by 2.

Radius (r) = diameter / 2 = 24 cm / 2 = 12 cm

Now, substitute the values into the formula for the volume:

2160 cubic cm = π * (12 cm)^2 * h

Simplifying the equation:

2160 = 144π * h

To isolate the height (h), divide both sides of the equation by 144π:

2160 / (144π) = h

Now calculate the value of h using a calculator:

h ≈ 4.78 cm

Therefore, the height of the cylindrical container is approximately 4.78 cm.

Thanks to solve my problem