Ok, let's first get our formulae for the volumes. These are given in the formula booklet, I believe.
Cone:
Vc=31πhr2Sphere:
VS=34πr3 therefore half a sphere would be
Vs=32πr3We want to find the volume of the entire shape. We are told the volume of the cone therefore we only need to work out the volume of the hemisphere.
What information do we need to work out the hemisphere? Well, by the looks of the equation we only need to find the radius of the hemishere.
How do we find the radius? For this we can use the volume and height of the cone so help us. We are told that the volume is
270πcm
3, and that the height is 10cm.
Since we know both of these, we can plug them into the equation of the cone giving us:
270π=31π⋅10⋅r2We can see that pi cancels and we can solve for the radius. Once we know the radius, it's only the matter of referring back to what we said before and plugging it into the hemisphere volume formula to find that.
Once we have the volume of the hemisphere, we can add that onto the volume of the cone and we get the overall volume of the solid shape.
Important note: The question asks you to give your answers in terms of
π. This means that rather writing out something like
2⋅3π as 18.849... we instead leave our answer as
6π. No need to convert into decimals.