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=(4)/(3)\pi\cdot r^3=(4)/(3)\pi\cdot1^3=(4)/(3)\pi\cdot1=(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