Problem 66 - Algebra 1

Question

A swimming pool is 50 meters long, 19.5 meters wide, and 3 meters deep. Use the formula for the volume of a rectangular prism to find the volume of water in the pool. The formula is the length times the width times the height.

Step-by-Step Solution

Answer

The volume of the swimming pool is 2925 cubic meters.

Step 1: Identify Given Values

The given values from the exercise are Length (L) = 50 m, Width (W) = 19.5 m and Height (H) = 3 m. These values will be plugged into the formula for volume of a rectangular prism.

Step 2: Apply the Formula

The formula for finding the volume V of a rectangular prism is V = L x W x H. Substituting the given values gives V = 50 m x 19.5 m x 3 m.

Step 3: Calculate the Volume

After substituting the values into the formula, we then compute the multiplication to give us the volume. Thus, V = 2925 cubic meters.

Key Concepts

Understanding the Rectangular Prism

A rectangular prism is a three-dimensional shape with six flat faces, all rectangles. Think of it as a box or a brick. It's one of the most common shapes we find in the physical world. The swimming pool from the exercise can also be seen as a massive rectangular prism, filled with water.

Each face of a rectangular prism consists of two sets of parallel rectangles. This means that opposite faces are identical in dimensions. In terms of measurements, a rectangular prism has a length, a width, and a height.

For instance:

• Length: This is the longest side between the two rectangular faces.
• Width: This is the shorter side along the base or top of the prism.
• Height: This is how tall the prism is, from the base to the top.

Understanding these dimensions is key to computing the volume of the rectangular prism, which is a fundamental concept in geometry.

The Role of Geometry in Volume Calculation

Geometry, the study of shapes and their properties, helps us understand how the world fits together. It's essential for solving many everyday problems, like our exercise of determining the volume of a swimming pool.

Calculating the volume of a rectangular prism falls under the geometry domain because it involves understanding three dimensions. Volume is defined as the amount of space occupied by an object, and in the case of a swimming pool, it's the water capacity we need to determine.

The formula for the volume of a rectangular prism is quite simple yet powerful: \[ V = L \times W \times H \]

This lets us multiply the length, width, and height to find how much space the prism encloses. For students, mastering this formula involves understanding how each term contributes to the total volume and visualizing how these dimensions come together to fill space.

Mathematics Education and Practical Applications

Mathematics education involves learning concepts that enable us to solve real-world problems effectively. It's not just about numbers but understanding how these numbers interact in our environment. In many schools, teaching volume calculation with geometric shapes like rectangular prisms is part of the curriculum.

This type of exercise helps students realize how theoretical knowledge applies to practical scenarios, such as estimating the water required for a pool or determining the amount of material needed to build a box.

To help students retain these concepts, educators often use:

• Visual Aids: Diagrams or 3D models to represent shapes.
• Hands-On Activities: Like measuring actual boxes to understand dimension and volume.
• Real-Life Examples: Such as the swimming pool exercise, making math tangible.

By integrating these methods, mathematics education becomes a tool not just for solving equations but for understanding and navigating the world around us.