Last weekend Ali visited an aviation festival near his neighborhood. In an experiment at the festival, an engineer introduced the element rhenium, which is used to make jet engine parts. The engineer showed the onlookers a small pyramid-shaped part of the element. The part was obtained by cutting one corner of a cube with edges of length centimeters as shown.
What is the density of rhenium?Ali wonders.
Maya is running a population census for her home city. She estimates the number of people in a region with a mile radius to be around
Population Density: About people per square mile
Explanation: See solution.
Since water has a greater density than cooking oil and the volumes of the bottles are the same, the bottle of water is heavier than the bottle of oil. The heavier bottle of water is being held in her right hand. Therefore, Izabella has found herself leaning to the right.
Diego, a bee-loving biology student, discovers that the depth of a hexagonal cell is centimeters, and its base has a side length of centimeters. Help Diego answer his following research questions.
As the diagram indicates, the base of the hollow part is a square with a side length of centimeters. Additionally, the mold is a cube with an edge length of centimeters. Therefore, the hollow is a square prism with a base edge length of centimeters and height of centimeters.
The diagram shows a water tank that is positioned horizontally with some water inside. The water level height is inches, and the distance between two bases is inches.
Kevin wonders how high the water level will rise when the tank is positioned vertically. Help Kevin to find it by answering the following questions.
Since the height of a solid is the distance between its bases, multiplying by will give the volume of the portion of the cylinder.
The difference between these volumes gives the volume of the water in the tank.Now suppose the tank is positioned vertically. The water level in the tank can be shown as follows.
After discussing hexagonal cells of beehives, Diego thinks he can approximate the number of cells in his body. His teacher recommends for Diego to treat a cell like a sphere with a diameter of centimeters.
If Diego's weight is kilograms and the density of a cell is approximately the density of water, which is gram per cubic centimeter, help Diego approximate the number of cells in his body. Write the answer in scientific notation.
To find the number of cells Diego's weight should be divided by the mass of a cell Recall that the density of a substance is equal to its mass divided by its volume. In other words, the mass of a substance is its density times its volume. Since the density of a cell is given, the volume of a cell can be calculated first.
The density of a cell is and its volume is By multiplying these values, the mass of a cell can be found.
Write in scientific notation
Throughout the lesson, different cases involving concepts of density based on area and volume have been discussed. Considering these situations, the challenge presented at the beginning of the lesson can be solved.
Ali knows that the small pyramid-shaped part of the element was obtained by cutting one corner of a cube with edges of length centimeters.