I have two problems that I'm stumped on. I know the correct anwers but I'm having problems coming up with the co rrect anwsers. Here are the problems:
1) Magnesium has a density of 1.7g/cm^3 and iron has density of 7.9 g/cm^3. A block of iron has a mass of 819g. What is the mass of a block of magnesium that has the same volume as the block of iron?
I used the formula Density = Mass/volume x 1/0.001. My handout shows the answer as being 1.8 x 10^2g, but i can't get it using the above.
2) Calculate the number of cubic centimeters in a rectangular box 0.0385m long, 4.6cm wide, and 0.000078 km thick. I converted the "0.385m' TO 385, 0.000078km thick to 0.0078 and multiplied all numbers but again I'm stupmped. My handout shows the correct answer as being 14,000 cm^3.
What steps were taken to solve this problems?
Thanks!
massblock= 819g*1.7/7.9=1.8E2g
0.0385m= 3.85cm
.000 078km= .078m=7.8cm
I get volume to be 140cm^3
To solve these problems, let's break down each step and explain how to arrive at the correct answers.
1) Problem: What is the mass of a block of magnesium that has the same volume as a block of iron?
Given information:
Density of magnesium (Mg) = 1.7 g/cm^3
Density of iron (Fe) = 7.9 g/cm^3
Mass of iron (Fe) = 819 g
Formula: Density = Mass/Volume
To find the mass of the magnesium block, we need to find its volume first. Since the volume of the magnesium block equals the volume of the iron block, we can set up an equation using the density formula:
Density of magnesium (Mg) = Mass of magnesium (Mg) / Volume of magnesium (Mg)
Density of iron (Fe) = Mass of iron (Fe) / Volume of iron (Fe)
We can rearrange the equations to solve for the volume of the magnesium block:
Volume of magnesium (Mg) = Mass of magnesium (Mg) / Density of magnesium (Mg)
Volume of iron (Fe) = Mass of iron (Fe) / Density of iron (Fe)
Since the volume of the magnesium and iron blocks is the same, we can equate these two equations:
Mass of magnesium (Mg) / Density of magnesium (Mg) = Mass of iron (Fe) / Density of iron (Fe)
Now we can solve the equation for the mass of magnesium:
Mass of magnesium (Mg) = (Mass of iron (Fe) x Density of magnesium (Mg)) / Density of iron (Fe)
Mass of magnesium (Mg) = (819 g x 1.7 g/cm^3) / 7.9 g/cm^3
Mass of magnesium (Mg) = 1.8 x 10^2 g
Therefore, the mass of the block of magnesium with the same volume as the block of iron is 1.8 x 10^2 g.
2) Problem: Calculate the number of cubic centimeters in a rectangular box.
Given information:
Length = 0.0385 m
Width = 4.6 cm
Thickness = 0.000078 km
We need to convert all the units to the same base unit, centimeters (cm), to make the calculation easier.
Length: 0.0385 m x 100 cm/m = 3.85 cm
Thickness: 0.000078 km x 100000 cm/km = 7.8 cm
Now, we can calculate the volume of the rectangular box:
Volume = Length x Width x Thickness
Volume = 3.85 cm x 4.6 cm x 7.8 cm
Volume = 134.748 cm^3
Therefore, the number of cubic centimeters in the rectangular box is 134.748 cm^3 (rounded to three decimal places).
It seems there might be errors or misunderstandings in your handout's answers, as the correct solutions are different from what you mentioned.