2020 HCI CT P3 Q4

The diagram below shows the curve \({{\left( y+5 \right)}^{2}}=-x-3\) and the line \(y=-x-10\). The curve intersects the line at coordinates \(\left( -7,-3 \right)\) and \(\left( -4,-6 \right)\). The region \(R\) is bounded by the curve and the line. Find the volume of the solid of revolution when \(R\) is rotated through four right angles about the \(x\)-axis.[4]