# Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.

Result

V =  18984.5 dm3
S =  3441.5 dm2

#### Solution:

$\ \\ v_2 = \dfrac{ | r_1^2-r_2^2+v^2 | }{2v} = \dfrac{ | 31^2-92^2+25^2 | }{2 \cdot 25} = 137.56 cm \ \\ r = \sqrt{ r_2^2 + v_2^2 } = \sqrt{ 92^2 + 137.56^2} = 165.49 cm \ \\ \ \\ V = \dfrac{4}{3} \pi r^3 = \dfrac{4}{3 \cdot 1000 } \pi \cdot 165.49^3 = 18984.5 \ dm^3$
$S = 4 \pi r^2 = \dfrac{ 4\pi \cdot 165.49^2}{100} = 3441.5 \ dm^2$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Do you want to convert area units? Do you want to convert length units? Do you know the volume and unit volume, and want to convert volume units? Pythagorean theorem is the base for the right triangle calculator.

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