A cylindrical jug that carries 1.5 ℓof water when it is filled to the brim has a base surface with the diameter
of 12 cm. How long is the jug?
Volume = π r^2 h
since 1.5 L = 1500 cm^3 of water
1500 = π(6^2)(h) , where h is the height of the cylinder.
h = 1500/(36π) = ....
To find the length of the jug, we need to find its height.
First, let's find the radius of the base of the jug. The diameter is given as 12 cm, and since the diameter is twice the radius, the radius would be half of that: 12 cm / 2 = 6 cm.
Next, we need to find the volume of the jug. The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
In this case, the volume is given as 1.5 liters. We need to convert this value to cubic centimeters because the radius and height are given in centimeters. 1 liter is equal to 1000 cubic centimeters, so 1.5 liters would be 1.5 * 1000 = 1500 cubic centimeters.
Substituting the known values into the cylinder volume formula, we have: 1500 = π * (6^2) * h.
Simplifying this equation, we get: 1500 = 36π * h.
To solve for h, we can divide both sides of the equation by 36π: 1500 / (36π) ≈ 13.18 cm.
Therefore, the height (or length) of the jug is approximately 13.18 cm.