Question

A water sample shows 0.009 grams of some trace element for every cubic centimeter of water. Jai uses a container in the shape of a right cylinder with a radius of 9.2 cm and a height of 12.6 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Jai collected? Round your answer to the nearest tenth.

Answer 1

Using the volume of a cylinder formula, we calculate the volume of water in Jai's container and then multiply by the mass proportion of the trace element to determine that Jai has collected approximately 30.2 grams of the trace element.

Step-by-step explanation:

To find out how much of the trace element Jai has collected in the second water sample, we must first calculate the volume of water in the cylinder-shaped container and then use the proportion of the trace element to determine its mass in the sample.

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius, and h is the height of the cylinder. In this case, r = 9.2 cm and h = 12.6 cm, so the volume of water that Jai collected is π(9.2 cm)²(12.6 cm). Plugging the values into the formula gives the volume of water in the cylinder.

Once we have the volume of water, we can calculate the mass of the trace element by multiplying the volume with the given mass proportion of the trace element (0.009 grams per cubic centimeter).

V = 3.14159 * (9.2 cm)² * 12.6 cm ≈ 3.14159 * 84.64 cm² * 12.6 cm ≈ 3357.339 cm³

The mass of the trace element in Jai's sample is approximately:

Mass = 3357.339 cm³ * 0.009 g/cm³ ≈ 30.216 g

After rounding to the nearest tenth, Jai has collected approximately 30.2 grams of the trace element.