A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 140 cm3, find the volume of the gap between the cylinder and the sphere.
Accepted Solution
A:
----------------------------------------------------------- Find Radius : ----------------------------------------------------------- [tex]\text {Volume of a sphere =} \dfrac{4}{3} \pi r^3[/tex]
[tex] \dfrac{4}{3} \pi r^3 = 140[/tex]
[tex]\pi r^3 = 140 \times \dfrac{3}{4}[/tex]
[tex]\pi r^3 = 105[/tex]
[tex]r^3 = \dfrac{105}{ \pi} [/tex]
[tex]r = 3.22 \ cm[/tex]
----------------------------------------------------------- Find volume of the cylinder : ----------------------------------------------------------- [tex]\text {Volume of the cylinder = } \pi r^2h[/tex]
[tex]\text {Volume of the cylinder = } \pi ((3.22)^2(3.22 \times 2)[/tex]
[tex]\text {Volume of the cylinder = } 209.77 \ cm^3[/tex]
----------------------------------------------------------- Find volume of the gap : ----------------------------------------------------------- [tex]\text {Volume of gap = } 209.77 - 140[/tex]