Volume do Prisma - Brasil Escola

Summary

In this video lesson, the teacher explains how to calculate the volume of a prism, emphasizing the formula: volume = base area × height. He demonstrates with examples such as a triangular base, square base, and pentagonal base prisms. The lesson also covers real-life applications, such as calculating the perimeter of a square base and determining the amount of algicide required for a swimming pool with varying depths. The teacher highlights the importance of understanding the formula and applying it to different shapes and practical scenarios.

Takeaways

• 😀 The volume of a prism is calculated as the area of the base multiplied by the height.
• 😀 Different types of prisms (triangular, square, pentagonal) follow the same volume formula: Volume = Area of base × Height.
• 😀 Understanding the volume formula for prisms helps simplify complex shapes by breaking them down into basic geometric calculations.
• 😀 In a square-based prism, the perimeter of the base can be found by calculating the side length (using the volume formula) and multiplying by 4.
• 😀 To calculate the perimeter of a square base, first determine the side length, then apply the formula: Perimeter = 4 × side length.
• 😀 The volume of a pool with different depths can be calculated by dividing the shape into simpler prisms and summing their volumes.
• 😀 When calculating the amount of chemical (e.g., algicide) to add to a pool, the volume of the pool must be converted from cubic meters to liters.
• 😀 For each cubic meter of water, 5 ml of algicide is needed, making it crucial to know the exact volume of the pool for correct application.
• 😀 In the pool example, the total volume is found by calculating the volume of each rectangular section (parallelepiped) and summing the results.
• 😀 Always remember that the formula for calculating the volume of any prism is simply the base area multiplied by the height, making it a versatile calculation for many shapes.

Q & A

What is the formula for calculating the volume of a prism?

The volume of a prism is calculated by multiplying the area of the base by the height. The formula is V = AB × H, where V is the volume, AB is the area of the base, and H is the height.

How is the volume of a triangular prism calculated?

The volume of a triangular prism is calculated by multiplying the area of the triangular base by the height of the prism. The formula is V = (1/2 × base × height of the triangle) × height of the prism.

How do you calculate the volume of a prism with a square base?

For a prism with a square base, the volume is calculated by squaring the side length of the base and multiplying it by the height. The formula is V = side² × height.

What does the perimeter of a square base of a prism represent?

The perimeter of the square base of a prism represents the total length of the four sides of the square. It is calculated by multiplying the side length by 4.

In the example with the square base prism, what is the value of the side length (x)?

The side length of the square base is found to be 5 cm after solving the equation, which is derived from the given volume and height.

How is the perimeter of the square base calculated in the example?

The perimeter is calculated by multiplying the side length (5 cm) by 4, resulting in a perimeter of 20 cm.

What is the volume of a pool with two depths separated by a step, and how is it calculated?

The volume of the pool is calculated by dividing the shape into two rectangular prisms and calculating the volume of each one. The total volume is the sum of these two volumes.

How do you calculate the volume of a pool with two different depths?

To calculate the volume, divide the pool into two sections with different depths. Then, calculate the volume for each section using the formula for the volume of a rectangular prism (length × width × height) and add the results.

How much algicide is needed for a pool with a specific volume of water?

The amount of algicide needed is calculated by multiplying the volume of water in liters by 5 ml per 1000 liters. For the pool with a volume of 85.2 cubic meters (or 85,200 liters), 426 ml of algicide is required.

How do you convert the volume of water from cubic meters to liters?

To convert cubic meters to liters, multiply the volume in cubic meters by 1000, as 1 cubic meter equals 1000 liters.