# 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:

$r^2 = 60^2+34^2 = 4756 \ \\ r = 68.96 \ mm \ \\ S = 4\pi r^2 = 4 \pi \cdot 4756 = 597.66 \ \text{cm}^2$
$V = \dfrac43 \pi r^3 = \dfrac43 \pi\cdot 68.96^3 = 1373.89 \ \text{cm}^3$

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