Question

A rectangular bar of platinum has a width of 5 centimeters, a height of 8 centimeters, and an unknown length. You measure the platinum bar and it is exactly 1 kilogram. Find the length of the bar if you know its density is 21.4 g/cm3 . Round your answer to the nearest hundredth.(1 point)

Answer 1

To find the length of the platinum bar, we can use the relationship between mass, density, and volume.

The formula for density is:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

Rearranging this formula gives:

\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

Given:
- Mass = 1 kg = 1000 g (since 1 kg = 1000 g)
- Density = 21.4 g/cm³

Now, we can calculate the volume of the platinum bar:

\[
\text{Volume} = \frac{1000 \text{ g}}{21.4 \text{ g/cm}^3} \approx 46.73 \text{ cm}^3
\]

Next, the volume of a rectangular prism (like our rectangular bar) is given by the formula:

\[
\text{Volume} = \text{Width} \times \text{Height} \times \text{Length}
\]

Plugging in the known values:

\[
46.73 \text{ cm}^3 = 5 \text{ cm} \times 8 \text{ cm} \times \text{Length}
\]

Calculating the area of the base:

\[
5 \text{ cm} \times 8 \text{ cm} = 40 \text{ cm}^2
\]

Now we have:

\[
46.73 \text{ cm}^3 = 40 \text{ cm}^2 \times \text{Length}
\]

To find the length, divide both sides by 40 cm²:

\[
\text{Length} = \frac{46.73 \text{ cm}^3}{40 \text{ cm}^2} \approx 1.16825 \text{ cm}
\]

Rounding to the nearest hundredth:

\[
\text{Length} \approx 1.17 \text{ cm}
\]

Thus, the length of the platinum bar is approximately **1.17 cm**.