Video: Finding the Volume of a Cone given Its Height and Base Radius

Determine the volume of the given solid to the nearest hundredth.

02:31

Video Transcript

Determine the volume of the given solid to the nearest hundredth.

Here, we can see the solid is a combination of two cones stuck together. We have this blue cone and we also have this pink cone. So in order to find the volume of this solid, we need to add together the volume of the blue cone and the volume of the pink cone. And since they are both cones, we need the volume of a cone formula. And it is one-third times 𝜋 times the radius squared times the height of the cone.

This means for each cone, we need to find the radius and the height. A radius will go from the center of the circle to a point on the circle. And here they share the same radius and it is 21 millimetres. Another last measurement that we need to find is the height of each cone. And these ones are actually different. The height of the blue cone can be found on the left. It is perpendicular to the circular base and it is 23 millimetres. And now the height of the pink cone is 26 millimetres.

And now, we can begin multiplying. However, we need to round to the nearest hundredth. So we want to be as exact as possible. So notice that we have 𝜋 twice in our equation. So instead of multiplying by 𝜋 and having to round two times, that’s gonna cause a bigger rounding error. So what we will do is leave 𝜋 until the very last step and then multiply by 𝜋 at the very end. So we’re only rounding once.

So we will multiply these numbers, but leave 𝜋 out — just write it next to the number — and the same here. So we have 3381𝜋 plus 3822𝜋, which is equal to 7203𝜋. And now, we multiply by 𝜋, which is approximately 22628.8918.

However, we need to round to the nearest hundredth. So we either need to keep the nine a nine or round up. So we look at the one and one is less than five. So we will keep the nine a nine, making our volume 22628.89 millimetres cubed.

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