# How do I calculate the amount from the volume?

• MHB
• Math_312 46
In summary: Ah, I see. so if I convert 6.5 e 21 nm² to m², which then becomes 65000 m². Is this the answer...Yes, that is the answer.

#### Math_312 46

The gold pavilion in the city of Kyoto is covered with gold leaf. Gold leaf has a thickness of 100 nm (nanometres) and is made from gold bars. A gold bar has a volume of 0.65 dm^3. How many square metres can the gold leaf from a gold bar cover?

The gold leaf is (presumably) a rectangular solid, ie, flat. So V = Ah.

-Dan

Math_312 46 said:
The gold pavilion in the city of Kyoto is covered with gold leaf. Gold leaf has a thickness of 100 nm (nanometres) and is made from gold bars. A gold bar has a volume of 0.65 dm^3. How many square metres can the gold leaf from a gold bar cover?
Your first task should be to express everything in the same units. So how many nm are there in a dm?

Next step: how many nm^3 in a dm^3? (You'll be getting some large powers of 10 at this stage.)

If the volume of a gold bar is X nm^3 then the formula V=Ah (with H = 100nm) tells you that the area covered by the gold leaf will be given by 100A = X.

Finally, that area A is in units of nm^2. You need to convert that to m^2 to get the result in square metres.

Opalg said:
Your first task should be to express everything in the same units. So how many nm are there in a dm?

Next step: how many nm^3 in a dm^3? (You'll be getting some large powers of 10 at this stage.)

If the volume of a gold bar is X nm^3 then the formula V=Ah (with H = 100nm) tells you that the area covered by the gold leaf will be given by 100A = X.

Finally, that area A is in units of nm^2. You need to convert that to m^2 to get the result in square metres.
If this is wrong can you help me?

Math_312 46 said:
That really doesn't seem very likely, does it? In fact, 0.01m^2 is one hundredth of a square metre. That is less than the size of a sheet of paper. If you take a gold bar and hammer it out until it is microscopically thin (which is what gold leaf is), you would expect it to cover quite a large area, certainly many hundreds of square metres.
Math_312 46 said:
If this is wrong can you help me?
A decimetre (dm) is one tenth of a metre. A nanometre (nm) is one billionth of a metre. So there are $10^9$ nm in a metre, and therefore $10^8$ nm in a dm. When you cube that in order to get a measure of volume, you find that there are $10^{24}$ nm^3 in a dm^3. So a volume of $0.65$ dm^3 is equal to $0.65\times10^{24}$ (or equivalently $6.5\times10^{23}$) nm^3.

Can you continue from there?

Opalg said:
That really doesn't seem very likely, does it? In fact, 0.01m^2 is one hundredth of a square metre. That is less than the size of a sheet of paper. If you take a gold bar and hammer it out until it is microscopically thin (which is what gold leaf is), you would expect it to cover quite a large area, certainly many hundreds of square metres.

A decimetre (dm) is one tenth of a metre. A nanometre (nm) is one billionth of a metre. So there are $10^9$ nm in a metre, and therefore $10^8$ nm in a dm. When you cube that in order to get a measure of volume, you find that there are $10^{24}$ nm^3 in a dm^3. So a volume of $0.65$ dm^3 is equal to $0.65\times10^{24}$ (or equivalently $6.5\times10^{23}$) nm^3.

Can you continue from there?

Sorry in advance but I find maths very difficult. But according to my calculations based on your explanation, it came out like this:

6.5 x 10^23 / 100 = 65 e 21 (65 and 21 zeros)

And thus I get the answer that 65 e 21nm² can the gold leaf of a gold bar cover?

Math_312 46 said:
Sorry in advance but I find maths very difficult. But according to my calculations based on your explanation, it came out like this:

6.5 x 10^23 / 100 = 65 e 21 (65 and 21 zeros)

And thus I get the answer that 65 e 21nm² can the gold leaf of a gold bar cover?
You left out the decimal point, so it should be 6.5 e 21 nm^2. But the question asks for the answer in square metres, so you still have to divide by $\bigl(10^9\bigr)^2 = 10^{18}$ to get the answer in those units.

Opalg said:
You left out the decimal point, so it should be 6.5 e 21 nm^2. But the question asks for the answer in square metres, so you still have to divide by $\bigl(10^9\bigr)^2 = 10^{18}$ to get the answer in those units.

Ah, I see. so if I convert 6.5 e 21 nm² to m², which then becomes 65000 m². Is this the answer or is something wrong?

Math_312 46 said:
Ah, I see. so if I convert 6.5 e 21 nm² to m², which then becomes 65000 m². Is this the answer or is something wrong?
Nearly there! You have one too many zeros. It should be 6.5 e 3 = 6500 m^2.

Opalg said:
Nearly there! You have one too many zeroes. It should be 6.5 e 3 = 6500 m^2.

So to be sure the answer is 6500 m^2 of the whole question?

Math_312 46 said:
So to be sure the answer is 6500 m^2 of the whole question?
Yes. :)

Opalg said:
Yes. :)

Thank you so much, you are a lifesaver:love:

I don't want to sound annoying, but when I was trying to solve another difficult task, I was stuck on how to figure out the lineup itself.

10.2 n + 10.8 2n / n + 2n

Question: In a survey, several measurements were taken and the average of the measurements was 10.2. In a new survey, twice as many measurements were taken and the mean of these measurements was 10.8. What is the mean of all the measurements?

It's all right if you don't want to help me with another question.

## 1. How do I convert volume to mass?

To convert volume to mass, you will need to know the density of the substance. The formula for calculating mass from volume is: mass = volume x density. Make sure to use consistent units for both volume and density.

## 2. How do I calculate the volume of an irregularly shaped object?

You can calculate the volume of an irregularly shaped object by using the displacement method. Fill a graduated cylinder with a known amount of water, then carefully place the object in the cylinder. The difference in the water level before and after the object is submerged will give you the volume of the object.

## 3. How do I convert from cubic inches to cubic centimeters?

To convert from cubic inches to cubic centimeters, you will need to multiply the number of cubic inches by 16.387. This is because 1 cubic inch is equal to 16.387 cubic centimeters.

## 4. How do I calculate the volume of a cylinder?

The formula for calculating the volume of a cylinder is: V = πr2h, where r is the radius of the cylinder and h is the height. Make sure to use consistent units for both the radius and height.

## 5. How do I convert from milliliters to liters?

To convert from milliliters to liters, you will need to divide the number of milliliters by 1000. This is because 1 liter is equal to 1000 milliliters.