The diagram shows sphere with centre $O$ and a total surface area of $\frac{192\pi}{3}$ \(\text{

Question

The diagram shows sphere with centre $O$ and a total surface area of $\frac{192\pi}{3}$ $\text{cm}^2$. Vertices of an equilateral triangle $ABC$ are on the surface of the sphere. Given that $AB = 2$ $\text{cm}$, find the total surface area of pyramid $O-ABC$, the volume of pyramid $O-ABC$, leaving your answers in the exact form.

Accepted Answer

(i) $\sqrt3(1+3\sqrt5)\text{ cm}^2$ (ii) $\frac{2\sqrt{11}}{3}\text{ cm}^3$

IP2U11 HOT Q4

IP2U11 HOT Q4

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