Question

A cylindrical measuring jug has a total volume of 500 ml and its radius is 3 cm. There are markings on the jug to show every 100 ml. What is the distance, in cm, between each of these markings?

Answer 1

5

Explanation:

To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:

0.5 liters = π * (3 cm)^2 * h

h = 0.5 liters / π * (3 cm)^2

h = 0.5 liters / 9π cm^2

Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:

Marking height = h / 5

= 0.5 liters / 9π cm^2 / 5

= 0.1 liters / 9π cm^2

So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.

Answer 2

The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:

0.5 liters = 0.5 x 10 cm^3 = 500 cm^3

V = πr^2h

500 = π x (3 cm)^2 x h

h = 500 / (π x (3 cm)^2)

Approximating π as 3.14, we get:

h = 500 / (3.14 x (3 cm)^2)

h = 500 / (3.14 x 9 cm^2)

h = 500 / 28.26 cm^2

h = 17.67 cm

So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.

Explanation: