Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.

Correct result:

S =  597.66 cm²
V =  1373.89 cm³

Solution:

$$\begin{gathered} r^2=60^2+34^2=4756 \\ r=68.96mm \\ S=4\pi r^2=4\pi \cdot 4756=597.66{\text{cm}}^2 \end{gathered}$$

$V={\displaystyle \frac{4}{3}}\pi r^3={\displaystyle \frac{4}{3}}\pi \cdot 68.96^3=1373.89{\text{cm}}^3$

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