# Solve: Distance, Velocity, Density and Volume

Questions:

1. If the sun which is 93,000,000 miles away away from Earth was to go out, how long would it take for us to know that this had happened? Light travels at a speed of 3 x 10^8 meters/second.

2. What would the density be (in g/cm^3) of a block that is 4 cm by 15 cm by 12 cm, and has a mass of 4.3 kg?

3. An object has a density of 8.96 g/cm^3. It has a mass of 405 grams. What is its volume?

4. An object has a density of 3.75 g/cm^3. It has a volume of 9.3 liters. What is its mass?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. To solve this problem we must convert the distance from miles to meters or kilometers.

We know 5 miles = 8 Km ===> 1 mile = 8/5 Km = 1.6Km

Thus the distance from earth to sun is,

D = 93,000,000 * 1.6 Km = 93,000,000 * 1.6 * 1000 meters

= 93 * 10^6 * 1.6 * 10^3 = 148.8 * 10^9 meters

Suppose, the last light pule from the sun leaves it at t=0 and that pulse will be our last detected light from the sun. The pulse travels with a speed of 3 * 10^8 m/s and has to cover a distance D. It will take a time to reach the earth. This time is the required answer to our question.

We have Velocity = Distance/Time

From this, Time = Distance/Velocity

Thus our answer is T = D/3*10^8

= 148.8 * 10^9 meters/3*10^8 = (148.8/3) * 10 = 496 Sec

Or, T = 496/60 = 8.26 Minutes

2. Density is defined to be the ratio of mass to volume. Here also remember to put the numbers in the same units.

Density = Mass/Volume

First, the volume of the block = 4 * 15 * 12 = 720 cm^3

Mass of the block = 4.3Kg = 4.3*10^3 Grams

Now density of the block = 4.3*10^3g/720cm^3 = 5.972 g/cm^3

3. Here also we will use the definition of density

From above answer, Volume = Mass/Density

= 405grams/(8.96g/cm^3) = 45.2 cm^3 ---Answer

4. Again, from answer to qn 3, Mass = Density * Volume

Remember to convert 9.3 Liters to cm^3

We have, 1 liter = 1000 cm^3

Thus, 9.3 liters = 9.3*10^3 cm^3

Now, Mass = (3.75g/cm^3) * 9.3*10^3 cm^3

= 34875 grams

= 34.875 Kg

If you are worried about recalling the formula mass/vol = density, try dimensional analysis to check the answer. For example, you can see that Mass/volume ==> number in grams/number in cm^3. Which yields the unit as g/cm^3 which is the unit of density. This method is the easiest way to check your answer to any question.

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