Solve for `a` given `8a^3+21=0.`
Round your answer to two decimal places. (2 marks)
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Solve for `a` given `8a^3+21=0.`
Round your answer to two decimal places. (2 marks)
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`a=-1.38`
| `8a^3+21` | `=0` |
| `8a^3` | `=-21` |
| `a^3` | `=-21/8` |
| `a` | `=-root3(21/8)` |
| `=-1.379…` | |
| `= -1.38` |
Solve for `p` given `64p^3+125=0.` (2 marks)
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`p=-5/4`
| `64p^3+125` | `=0` |
| `64p^3` | `=-125` |
| `p^3` | `=-125/64` |
| `p` | `=-root3(125/64)` |
| `=-(root3(125))/(root3(64))` | |
| `= -5/4` |
Solve for `x` given `8x^3=27`. (2 marks)
`x=3/2`
| `8x^3` | `=27` |
| `x^3` | `=27/8` |
| `x` | `=root3(27/8)` |
| `=(root3(27))/(root3(8))` | |
| `= 3/2` |
The volume of a sphere is given by `V = 4/3 pi r^3` where `r` is the radius of the sphere.
If the volume of a sphere is `220\ text(cm)^3`, find the radius, to 1 decimal place. (3 marks)
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`3.7\ \ text{cm (to 1 d.p.)}`
| `V` | `= 4/3 pi r^3` |
| `3V` | `= 4 pi r^3` |
| `r^3` | `= (3V)/(4 pi)` |
`text(When)\ \ V = 220`
| `r^3` | `= (3 xx 220)/(4 pi)` |
| `= 52.521…` | |
| `:. r` | `=root3 (52.521…)` |
| `= 3.744…\ \ \ text{(by calc)}` | |
| `= 3.7\ \ text{cm (to 1 d.p.)}` |
Make `r` the subject of the equation `V = 4/3 pir^3`. (3 marks)
`r = root(3)((3V)/(4pi))`
| `V` | `= 4/3 pir^3` |
| `3V` | `=4pir^3` |
| `(3V)/4` | `= pir^3` |
| `r^3` | `= (3V)/(4pi)` |
| `r` | `= root(3)((3V)/(4pi))` |