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A container in the shape of a sphere of radius 6cm is filled with water to depth of 10cm.
(a) Find the volume of the water
(b) If the water flows out through a small hole in the bottom so that the level drops 2cm, how much water escaped.
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Use the formula for the volume of a spherical cap
V = ,
where R is the radius of the sphere and h is the height (= the depth) of the cap.
This formula works uninterruptedly in the entire diapason from h= 0 (empty container) to h= 2R (full container).
So, in case (a) you apply the formula at R= 6 cm and h= 10 cm
V = = 837.76 cm^3. ANSWER
I case (b), the final volume is
V = = 670.21 cm^3.
The amount of water escaped is the difference 837.76 cm^3 - 670.21 cm^3 = 167.55 cm^3. ANSWER
Solved.
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For the formulas on the volume of a spherical cap see these Internet sources
https://mathworld.wolfram.com/SphericalCap.html
https://en.wikipedia.org/wiki/Spherical_cap