Answer to Question #287007 in Calculus for faith

Question

1. the inside of a wash basin is in the shape of segment of a sphere; the distance across the top is 18in. and its greatest depth is 7in. find how many pints of water it will hold, reckoning 7.48gal to the cubic foot.

Answer 1

$V = \frac{1}{3}\pi h^2(3R-h) \space \space$ [ the volume of the spherical cap]

$h = 7in \space \space \space R = \frac{18+7}{2}=12.5 in$

$V = \frac{1}{3}*3.14*49*(37.5-7)=1,564 \space \space cubic \space inches$

$V = 0.91 \space\space cubic \space foot$

$0.91*7.48 = 6.8 gal$