A plane vs. sphere

The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere.

Final Answer:

S =  502.6548 cm²
V =  1059.6894 cm³

Step-by-step explanation:

$$\begin{gathered} x=2\text{cm} \\ r=6\text{cm} \\ {R}^2=r^2+x^2 \\ R=\sqrt{r^2+x^2}=\sqrt{6^2+2^2}=2\sqrt{10}\text{cm}\doteq 6.3246\text{cm} \\ S=4\pi \cdot R^2=4\cdot 3.1416\cdot 6.3246^2=502.6548{\text{cm}}^2 \end{gathered}$$

$V=\frac{4}{3}\cdot \pi \cdot R^3=\frac{4}{3}\cdot 3.1416\cdot 6.3246^3=1059.6894{\text{cm}}^3$

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