CAHSEE practice: Problems 35-37 | CAHSEE | Khan Academy | Summary and Q&A

TL;DR

The content includes three mathematical problems related to area and volume calculations explained step-by-step.

Key Insights

• 🍹 In problem 35, finding the area of complicated figures can be simplified by dividing them into smaller rectangles and summing their individual areas.
• 🦶 Problem 36 demonstrates the conversion between square feet and acres using a given conversion factor.
• 🔇 Problem 37 highlights the importance of understanding the dimensions and counting units when calculating volumes of three-dimensional objects.
• 🍳 Mathematical problem-solving often involves breaking down complex problems into simpler steps for easier solution finding.
• 🖐️ Geometry concepts, such as areas of rectangles and volumes of prisms, play a significant role in these problem-solving examples.
• 🧑‍🏭 Conversion factors are useful in transforming measurements from one unit to another.
• 🦻 Visualization and counting techniques can aid in solving problems involving structures made up of repeated shapes.

Transcript

Problem 35. In the figure below, every angle is a right angle. So they're just saying that's a right angle, that's a right angle, these are all right angles. You get the idea. What is the area, in square units, of the figure? So the area. How can we figure this out? We can divide this up into a bunch of rectangles and figure out their respective ar... Read More

Questions & Answers

Q: How is the area of the figure in problem 35 determined?

The figure is divided into rectangles, and the area of each rectangle is calculated by multiplying its length and width. The sum of all the rectangle areas gives the total area of the figure, which is found to be 120 square units.

Q: What is the size of the field in problem 36 expressed in acres?

The dimensions of the field are multiplied to find the area in square feet, which is then divided by the conversion factor of 43,560 to obtain the area in acres. The field is determined to be approximately 2 acres.

Q: How is the volume of the object in problem 37 calculated?

Each rectangular prism in the object has the dimensions 5 cm by 3 cm by 2 cm. The volume of each prism is calculated by multiplying these dimensions, resulting in a volume of 30 cubic centimeters per prism. As there are 10 prisms in total, the volume of the entire object is 300 cubic centimeters.

Q: How does the calculation in problem 37 involve the structure depicted in plus sign or cross shape?

The structure shown is composed of a set of rectangular prisms. The count of these prisms is determined by counting the number of boxes in each layer and considering that there are two layers. The volume calculation then involves multiplying the number of prisms (10) by the volume of each prism (30 cubic centimeters).

Summary & Key Takeaways

• Problem 35: The figure consists of rectangles, and by finding the areas of each rectangle and adding them up, the total area of the figure is determined to be 120 square units.

• Problem 36: A rectangular field with dimensions 363 feet by 240 feet is given. The area of the field is calculated to be 87,120 square feet, which is approximately equal to 2 acres.

• Problem 37: An object made up of 10 rectangular prisms is shown. The volume of each prism is found to be 30 cubic centimeters, resulting in a total volume of 300 cubic centimeters.