Question

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.

Answer 1

-----------------------------------------------------------
Find Radius :
-----------------------------------------------------------

`\text {Volume of a sphere =} (4)/(3) \pi r^3`


`(4)/(3) \pi r^3 = 140`


`\pi r^3 = 140 * (3)/(4)`


`\pi r^3 = 105`


`r^3 = (105)/( \pi)`


`r = 3.22 \ cm`

-----------------------------------------------------------
Find volume of the cylinder :
-----------------------------------------------------------

`\text {Volume of the cylinder = } \pi r^2h`


`\text {Volume of the cylinder = } \pi ((3.22)^2(3.22 * 2)`


`\text {Volume of the cylinder = } 209.77 \ cm^3`

-----------------------------------------------------------
Find volume of the gap :
-----------------------------------------------------------

`\text {Volume of gap = } 209.77 - 140`


`\text {Volume of gap = } 69.77 \ cm^3`

-----------------------------------------------------------

`\bf \text {Answer : } 69.77 \cm^3`
-----------------------------------------------------------