Question Video: Solving Volume Problems Involving Spheres and Cylinders | Nagwa Question Video: Solving Volume Problems Involving Spheres and Cylinders | Nagwa

# Question Video: Solving Volume Problems Involving Spheres and Cylinders

Michael needs to produce lidless square-based boxes with a height of 4 inches and a volume of 320 cubic inches. He uses the net as seen in the given figure but needs to work out the value of 𝑥. Find 𝑥, giving your solution to two decimal places.

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### Video Transcript

Michael needs to produce lidless square-based boxes with a height of four inches and a volume of 320 cubic inches. He uses the net as seen in the given figure but needs to work out the value of 𝑥. Find 𝑥, giving your solution to two decimal places.

Well, what we know about the volume of a cuboid is that it is equal to the length multiplied by the width multiplied by the height. Well, as the boxes that Michael’s trying to produce are square based, we know that the length and the width are gonna be the same. And these both are going to be 𝑥. And we also know that the height is gonna be equal to four inches. So therefore, what we can say is that the volume is gonna be equal to 𝑥 multiplied by 𝑥 multiplied by four.

What we’re also told in the question is the volume itself cause we’re told that it’s 320 cubic inches. So what we can do is substitute this in to our equation. And when we do, what we’re gonna get is 320 is equal to four 𝑥 squared. That’s four multiplied by 𝑥 multiplied by 𝑥. So now what we can do is divide both sides of the equation by four. And when we do this, what we’re gonna get is 80 is equal to 𝑥 squared.

So then, if we want to find 𝑥, when we’re gonna need to do is take the square root of both sides. Well, when we do this, what we’re gonna get is 8.94427191 is equal to 𝑥. We could’ve also had a negative value. But we’re not interested in that because what we’re looking at is a length, and a length cannot be negative.

Well, have we finished here? Well, no, not quite because what we want to do is find 𝑥, giving the solution to two decimal places. So we need to do a bit of rounding. Well, if we’re gonna round it to two decimal places, what we do is we look at the second decimal place. Then we take a look at the digit to the right of it. This is our deciding digit. Because this is less than five, what we’re gonna do is round down. So we can say the value of 𝑥 is 8.94 inches, and that’s to two decimal places.

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