Question

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

Answer 1

To find the length of the platinum bar, we can use the formula for density:

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

We know the density of platinum is 21.4 g/cm³, and the mass of the bar is 1 kg, which is 1000 grams.

First, we rearrange the formula to find the volume:

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

Now, calculating the volume:

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

Next, we know the volume of a rectangular bar is given by:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

For this problem, we have:

- Width = 5 cm
- Height = unknown (we'll assume the height is the same as the width) = 5 cm

Now let's calculate the volume from the dimensions we have:

\[
\text{Volume} = \text{length} \times 5 \text{ cm} \times 5 \text{ cm}
\]

Substituting in the known values, we get:

\[
46.73 = \text{length} \times 5 \times 5
\]

This simplifies to:

\[
46.73 = \text{length} \times 25
\]

Now, we can find the length:

\[
\text{length} = \frac{46.73}{25} \approx 1.8692 \text{ cm}
\]

Rounding to the nearest hundredth:

\[
\text{length} \approx 1.87 \text{ cm}
\]

Thus, the length of the platinum bar is approximately **1.87 cm**.