The volume of a sphere is given by:
`V = frac(4)(3)pir^3`
What is the volume of a sphere of diameter 6 cm? Give your answer to 3 significant figures.
| For a sphere: | Volume | `= frac(4)(3)pir^3` |
| Substitute | `=frac(4)(3)pi(6)^3` | |
| `= 904.778` |
Answer: 905 cm3
A sphere and a cylinder have the same volume. If the radius of the sphere is 9cm, what is the height of the cylinder?
| Cylinder: | Volume | `= pir^2l` |
| Sphere: | Volume | `= frac(4)(3)pir^3` |
| Both equal | `pir^2l` | `= frac(4)(3)pir^3` |
| Divide both sides by `pi` | `r^2l` | `= frac(4)(3)r^3` |
| Divide both sides by `r^2` | `l` | `= frac(4)(3)r` |
| Substitute | `l` | `= frac(4)(3)(9)` |
| `= 12` |
Answer: 12 cm