Question

A 76.00 pound flask of mercury costs $150.50. The density of mercury is 13.534 g/cm3.It takes 4.800 in^3 of mercury to make one manometer. Find the price of the mercury used to make 21 manometers by first calculating the cost of mercury for one manometer.What is the price of mercury used to make one manometer?

Answer 1

Price of one pound of mercury is derived as follows;

`\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=(150.50)/(76) \\ \text{Price of 1 lb}=1.98 \end{gathered}`

This means 1 pound of mercury costs $1.98

1 pound = 453.6 grams

Therefore;

`\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}`

The price of 1 gram of mercury would be;

`\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=(1.98)/(453.6) \\ \text{Price of 1 gram}=0.004365 \end{gathered}`

This means 1 gram of mercury costs $0.004365

Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;

`\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534*0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}`

This means 1 cubic centimeter of mercury would cost $0.059

Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,

`\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387*0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}`

This means 1 cubic inch costs $0.9668

It takes 4.800 cubic inches to make 1 manometer.

Therefore, the cost of 4.800 cubic inches would be;

`\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668*4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}`

If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64

Therefore, to make 21 manometers, we would have;

`\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21*4.64 \\ 21\text{ manometers}=97.44 \end{gathered}`

ANSWER:

The price of mercury required to make 21 manometers would be $97.44