Question

A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside the cylinder to the nearest tenth of a cubic inch

Answer 1

first we find the volume of the cylinder

$V=\pi\cdot r^2\cdot h$

and diameter = 2 in, therefore the radius = 1 in, so

$V=\pi\cdot1^2\cdot5=\pi\cdot1\cdot5=5(3.14)=15.7$

volume of cylinder is 15.7 in^3

then, volume of the sphere is:

$V=\frac{4}{3}\pi\cdot r^3=\frac{4}{3}\pi\cdot1^3=\frac{4}{3}\pi\cdot1=\frac{4}{3}(3.14)=4.2$

volume of the sphere is 4.2 in^3, so the volume lying outside the sphere but inside the cylinder is:

$V=15.7-4.2=11.5$

answer: 11.5 in^3