For the first problem I would just take the volume of the whole cake, and multiply it by the required ratio. which is

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For the second problem you know that the circumference of the circle is and the slant height of the cone will equal the radius of the circle. So the circumference of the base of the cone will be of the circle's circumference. From that you can work out the radius of the cone. Since it is a right cone with it's vertex over the centre of it's base the equation relating it's radius, height and slant height is . From that you can work out the height. Then, knowing the height and the radius, you can calculate the volume of the cone.