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)
cm

Answer 1

To find the length of the platinum bar, we first need to use the given density and mass to find the volume.

Given:
- Mass of the platinum bar (m) = 1 kg = 1000 g (since 1 kg = 1000 g)
- Density of platinum (ρ) = 21.4 g/cm³

We can use the formula for density:

\[
\rho = \frac{m}{V}
\]

Rearranging this formula to solve for volume (V):

\[
V = \frac{m}{\rho}
\]

Substituting the values we have:

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

Next, we know the volume of a rectangular prism (or a rectangular bar) is given by the formula:

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

Let \( L \) be the unknown length of the bar. The width is 5 cm and the height is 8 cm, so:

\[
V = L \times 5 \, \text{cm} \times 8 \, \text{cm}
\]

Substituting the known values into the volume equation:

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

This simplifies to:

\[
46.73 = L \times 40
\]

Now, solving for \( L \):

\[
L = \frac{46.73}{40} \approx 1.16825
\]

Rounding to the nearest hundredth:

\[
L \approx 1.17 \, \text{cm}
\]

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