| Exam Board | OCR MEI |
|---|
| Module | Further Pure Core (Further Pure Core) |
|---|
| Year | 2024 |
|---|
| Session | June |
|---|
| Topic | Volumes of Revolution |
|---|
4 The equation of a curve is \(\mathrm { y } = \frac { 1 } { \sqrt { \mathrm {~K} ^ { 2 } + \mathrm { x } ^ { 2 } } }\), where \(k\) is a positive constant. The region between the \(x\)-axis, the \(y\)-axis and the line \(x = k\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
Given that the volume of the solid of revolution formed is 1 unit \({ } ^ { 3 }\), find the exact value of \(k\).