Cylindrical jug that carries 1.5 litre of water when it is filled to the brim has a base surface with the diameter of 12cm ..how long is the jug?
v = Bh
so, since 1L = 1000cm^3,
1500 = π*6^2 * h
h = 1500/(36π) = 13.27 cm
To determine the height or length of the cylindrical jug, we need to use the formula for the volume of a cylinder.
The volume of a cylinder is given by the formula: V = πr^2h,
where V is the volume, π is a mathematical constant, r is the radius of the base, and h is the height or length of the cylinder.
In this case, we are given the diameter of the base, which is 12 cm. The radius (r) can be found by dividing the diameter by 2:
r = 12 cm / 2 = 6 cm.
We also know that the jug carries 1.5 liters of water when filled to the brim. To find the height (h), we need to convert this volume to the corresponding unit.
1 liter = 1000 cm^3 (cubic centimeters).
So, 1.5 liters = 1.5 x 1000 cm^3 = 1500 cm^3.
Now, we can rearrange the formula to solve for the height (h):
V = πr^2h
1500 cm^3 = π(6 cm)^2h
Simplifying further:
1500 cm^3 = 36π cm^2h
To isolate h, divide both sides of the equation by 36π:
1500 cm^3 / (36π cm^2) = h
The value of π is approximately 3.14. So, dividing 1500 by (36 x 3.14) will give us the height (h) of the jug in centimeters.
h ≈ 1500 / (36 x 3.14) cm
Calculate the numerical value to find the height of the jug.
To find the length of the cylindrical jug, you need to determine the height.
1. Start by calculating the radius of the base. The diameter is given as 12 cm, so the radius is half of that:
radius = diameter / 2 = 12 cm / 2 = 6 cm.
2. Use the formula for the volume of a cylinder to find the height. The volume of the cylinder is given as 1.5 liters, which converts to 1500 cubic centimeters (since 1 liter = 1000 cubic centimeters). The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is the mathematical constant pi (approximately 3.14), r is the radius, and h is the height. Rearranging the formula, you can solve for h:
h = V / (π * r^2), where V = 1500 cm^3 and r = 6 cm.
h = 1500 cm^3 / (3.14 * 6 cm^2)
≈ 25.32 cm.
3. Therefore, the height of the cylindrical jug is approximately 25.32 cm.