A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre...

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A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre O and radius 12 cm. A is the vertex of the cone, B is a point on the base of the cone that touches the sphere and, C is the centre of the base of the cone. :0 Let |OC|=x. Find | BC|, the radius of the cone, in terms of x. (i) Show that the volume of the cone is equal to (12 + x)²(12 – x). (ii) (iii) Hence find the maximum volume of the cone, in terms of T. A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre O and radius 12 cm. A is the vertex of the cone, B is a point on the base of the cone that touches the sphere and, C is the centre of the base of the cone. :0 Let |OC|=x. Find | BC|, the radius of the cone, in terms of x. (i) Show that the volume of the cone is equal to (12 + x)²(12 – x). (ii) (iii) Hence find the maximum volume of the cone, in terms of T.

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i BC radius of the cone in terms of x Having ABC as a bigger triangle join B to ... View the full answer