Spherical cap

The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.

Correct result:

r =  8.9 cm

Solution:

a=8 cm h=5 cm  r2=a2+(rh)2 r2=a2+r22rh+h2 2rh=a2+h2  r=a2+h22 h=82+522 5=8910=8.9 cma=8 \ \text{cm} \ \\ h=5 \ \text{cm} \ \\ \ \\ r^2=a^2 + (r-h)^2 \ \\ r^2=a^2 + r^2-2rh + h^2 \ \\ 2rh=a^2 + h^2 \ \\ \ \\ r=\dfrac{ a^2 + h^2 }{ 2 \cdot \ h }=\dfrac{ 8^2 + 5^2 }{ 2 \cdot \ 5 }=\dfrac{ 89 }{ 10 }=8.9 \ \text{cm}



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