6K Capacity Part 3

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Summary

In this video, Mr. Bodgers tackles a challenging math question involving the calculation of water tank volume when the tank is 3/4 full. He walks viewers through the process using the formula for the volume of a cylinder, which is πr²h. With given measurements, the entire tank's volume is calculated first, and then the volume for the 3/4 full tank is determined. Finally, the volume in cubic meters is converted to liters, offering a comprehensive solution to the problem posed.

Highlights

Calculating full tank volume using the formula πr²h 🧮
Adjusting for the tank being 3/4 full by multiplying with 3/4 ➗
Converting from cubic meters to liters to finalize the solution ✖️

Key Takeaways

Understanding volume calculations for cylinders using πr²h formula 📐
Converting cubic meters to liters by multiplying with 1000 🔄
Appreciating precise calculations to three decimal points for accuracy 📏

Overview

Mr. Bodgers presents a math problem involving calculating the volume of a cylindrical water tank. The initial step involves using the volume formula for cylinders, πr²h, where the radius and height are inputted to derive the total volume of the tank.

The task is then refined by considering the tank is 3/4 full, which requires adjusting the full volume calculation. Mr. Bodgers expertly multiplies the total volume by 3/4 to ascertain the present water volume in the tank.

Finally, to provide the answer in liters, Mr. Bodgers converts cubic meter volume to liters by multiplying by 1000. He concludes with a neatly packaged solution, outlining the process clearly for viewers.

Chapters

00:00 - 00:30: Introduction In the introduction, the chapter addresses the challenge of calculating capacities, using the example of a water tank that is 3/4 full. The key task highlighted is to calculate the volume of the water tank in cubic meters, accurate to three decimal places. The approach involves treating the tank as a cylinder and applying the formula for the volume of a cylinder, which is volume equals πr²h.
00:30 - 02:00: Calculating Volume of the Whole Tank The chapter discusses the calculation of the volume of a cylindrical tank. The radius of the tank is given as 0.9 meters, and the height is 2.2 meters. Initially, these details are used to calculate the volume of the entire tank using the formula for the volume of a cylinder: π times the radius squared times height. Although it's mentioned that the tank is only 3/4 full, the focus remains on determining the volume of the whole tank.
02:00 - 03:00: Calculating Volume of Water in the Tank The chapter explains the process of calculating the volume of water in a tank. It involves using the formula for the volume of a cylinder, where the radius is squared and multiplied by Pi and the height of the cylinder. The specific example uses a radius of 0.9 and a height of 2.2, resulting in a final calculated volume of 5.598 cubic meters after carrying out the calculations to three decimal places.
03:00 - 03:30: Converting Cubic Meters to Litres The chapter covers the topic of converting cubic meters to liters in the context of calculating the volume of water in a tank. Initially, it determines the total capacity of the tank in cubic meters, which is the volume it can hold when full. It then progresses to solve a problem, Question B, which requires calculating the actual amount of water in the tank given that it is 3/4 full. The focus is on converting this measurement into liters to provide the solution.

6K Capacity Part 3 Transcription

00:00 - 00:30 you want to example to four capacities so this is our more challenging question and it's telling us that the following water tank is 3/4 full water right there question aces calculate the volume off the water tank in cubic meters correct to three decimal places so what we're going to do is I'm just going to eat like a normal cylinder and the volume of a cylinder is given by the formula volume equals PI R squared H also area
00:30 - 01:00 times height is the other one okay now the radius of this tank is 0.9 meters so we're going to go pi times 0.9 times height and the height is 2.2 in this case now did say at the beginning that it's only 3/4 full of water but we'll get to the owner set we're really just going to find the volume off the whole tank for now all right what is
01:00 - 01:30 that pi times 0.9 actually off main mistake this is point nine squared to 0.9 squared times 2.2 all right we get to three decimal places they want it so five point five nine eight cubic meters
01:30 - 02:00 now that that's the volume of the whole tank that's how much water whole tank can hold but they have asked you to calculate the volume off the water tip oh no you know that's right calculate the volume off the water tank of cubic meters all right you know that's fine it's neat it's really moving on to question B it says calculate the amount of water in the water tank and it wants you to give you a solution and leaders now because it's 3/4 full we're just
02:00 - 02:30 going to go three quarters and multiply that by five point five nine eight to see exactly how much water is in there now I get to three decimal places for point one nine nine meters cubed that's how much water isn't there now they want your solution in litres so we've got to go from meters cubed 2 liters let's look
02:30 - 03:00 back at the previous slide which tells you what to do if it's meters cubed and I want to go to litres it tells me two times by a thousand all right let's do that so four point one nine nine times one thousand equals four thousand one hundred and ninety nine litres that is
03:00 - 03:30 in this tank