You measure one edge of a cube using a meter stick marked in centimeters. Unfortunately, the edge is longer than 1 m. You mark the 1-m point on the cube edge with a pen and then, using a 15-cm ruler marked in millimeters, measure the remaining distance to be 1.40cm.
(a) What is the length of the edge in centimeters?
(b) What is the volume of the cube in cubic centimeters? (Remember, the lengths of all edges of a cube are equal.) Watch your significant figures. Use scientific notation if you have to.
(c) The cube has a mass of 111 kg. What is its density in grams per milliliter? Watch your significant figures.
I answered this below. You should check for answers before posting duplicates.
Actually, I did this for another student; however, you posted under that same question that you had the same problem. My answer to you is the same as to the other student.
Miranda and Sally are apparently the same person.
To solve this problem, we need to follow these steps:
(a) To find the length of the edge in centimeters, we first need to calculate the total length of the edge. We know that the 1-meter point on the cube edge is marked and the remaining distance is 1.40 cm.
The total length of the edge can be calculated by adding the measured length to the marked 1-meter point:
Total edge length = 1 meter + 1.40 cm
Before adding, we need to convert 1 meter to centimeters since our ruler is marked in centimeters:
1 meter = 100 centimeters
Now we can add the lengths together:
Total edge length = 100 cm + 1.40 cm = 101.40 cm
Therefore, the length of the edge is 101.40 centimeters.
(b) To find the volume of the cube in cubic centimeters, we can use the fact that the lengths of all edges of a cube are equal.
The volume of a cube can be calculated by raising the length of a side to the power of 3:
Volume = edge length ^ 3
Substituting the calculated edge length into the formula:
Volume = 101.40 cm ^ 3
By evaluating this expression, we find that the volume of the cube is 1,044,951.784 cubic centimeters.
(c) To find the density of the cube in grams per milliliter (g/mL), we need to know the mass and volume of the cube.
Given that the mass of the cube is 111 kg, we first need to convert it to grams since the density is typically expressed in g/mL:
1 kg = 1000 grams
Now we can calculate the density by dividing the mass (in grams) by the volume (in milliliters):
Density = mass / volume
To convert the volume from cubic centimeters to milliliters, we need to remember that 1 mL is equal to 1 cm³:
Density = 111,000 g / 1,044,951.784 mL
By performing the division and rounding to the appropriate significant figures, we find that the density of the cube is approximately 0.106 g/mL.