A sector with radius 10 cm and angle `theta` is used to form the curved surface of a cone with base radius `x` cm, as shown in the diagram.
The volume of a cone of radius `r` and height `h` is given by `V = 1/3 pi r^2 h`.
- Show that the volume, `V` cm³, of the cone described above is given by
`V = 1/3 pi x^2 sqrt(100 - x^2)`. (1 mark)
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- Show that `(dV)/(dx) = (pi x (200 - 3x^2))/(3 sqrt(100 - x^2))`. (2 marks)
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- Find the exact value of `theta` for which `V` is a maximum. (3 marks)
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