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 6 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 4-mile radius to be around 220000.
Population Density: About 4376 people per square mile
Explanation: See solution.
Diego, a bee-loving biology student, discovers that the depth of a hexagonal cell is 0.5 centimeters, and its base has a side length of 0.3 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 5 centimeters. Additionally, the mold is a cube with an edge length of 7 centimeters. Therefore, the hollow is a square prism with a base edge length of 5 centimeters and height of 7 centimeters.
The diagram shows a water tank that is positioned horizontally with some water inside. The water level height is 10 inches, and the distance between two bases is 50 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 50 will give the volume of the portion of the cylinder.
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 60 kilograms and the density of a cell is approximately the density of water, which is 1 gram per cubic centimeter, help Diego approximate the number of cells in his body. Write the answer in scientific notation.
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 6 centimeters.