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Math Help - advanced geometry volume problems

  1. #1
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    advanced geometry volume problems

    A cyndrilical cake has a 50 degree slice removed from it. the cake is 9 inches high and has a radius of 3 inches. what is the volume of the remaining cake?

    A circular piece of paper has a 90 degree sector removed from it. It is the rolled up into a cone. If the radius of the initial circle is 8 inches, what will be the volume of this resulting cone to the nearest cubic inch?
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  2. #2
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    For the first problem I would just take the volume of the whole cake, 9\pi 3^2 and multiply it by the required ratio. which is
    \frac{360}{360}-\frac{50}{360}=\frac{31}{36}.

    For the second problem you know that the circumference of the circle is 2\pi r 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 \frac{3}{4} 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 s=\sqrt{r^2+h^2}. From that you can work out the height. Then, knowing the height and the radius, you can calculate the volume of the cone.
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