a rectangular bar of platinum has a width of 5 centimeters, a height of 8 centimeters, and an unknown…

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)

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

Explanation:

Step1: Convert mass to grams

Since 1 kilogram = 1000 grams, the mass $m = 1000$ g.

Step2: Use density - volume formula

The density formula is $\rho=\frac{m}{V}$, where $\rho$ is density, $m$ is mass and $V$ is volume. We can re - arrange it to find volume $V=\frac{m}{\rho}$. Substituting $m = 1000$ g and $\rho=21.4$ g/cm³, we get $V=\frac{1000}{21.4}\text{ cm}^3\approx46.73$ cm³.

Step3: Use volume formula for rectangular bar

The volume of a rectangular bar (prism) is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. Given $w = 5$ cm and $h = 8$ cm, and $V\approx46.73$ cm³. We can re - arrange the formula to find length $l=\frac{V}{w\times h}$. Substituting the values, we have $l=\frac{46.73}{5\times8}=\frac{46.73}{40}=1.17$ cm.

Answer:

$1.17$ cm