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Determine the volume of the given solid to the nearest hundredth.
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Here, we can see the solid is a combination of two cones stuck together.
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We have this blue cone and we also have this pink cone.
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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.
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And since they are both cones, we need the volume of a cone formula.
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And it is one-third times π times the radius squared times the height of the cone.
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This means for each cone, we need to find the radius and the height.
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A radius will go from the center of the circle to a point on the circle.
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And here they share the same radius and it is 21 millimetres.
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Another last measurement that we need to find is the height of each cone.
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And these ones are actually different.
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The height of the blue cone can be found on the left.
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It is perpendicular to the circular base and it is 23 millimetres.
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And now the height of the pink cone is 26 millimetres.
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And now, we can begin multiplying.
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However, we need to round to the nearest hundredth.
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So we want to be as exact as possible.
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So notice that we have π twice in our equation.
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So instead of multiplying by π and having to round two times, thatβs gonna cause a bigger rounding error.
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So what we will do is leave π until the very last step and then multiply by π at the very end.
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So weβre only rounding once.
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So we will multiply these numbers, but leave π out β just write it next to the number β and the same here.
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So we have 3381π plus 3822π, which is equal to 7203π.
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And now, we multiply by π, which is approximately 22628.8918.
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However, we need to round to the nearest hundredth.
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So we either need to keep the nine a nine or round up.
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So we look at the one and one is less than five.
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So we will keep the nine a nine, making our volume 22628.89 millimetres cubed.