Question

• Find the volume of the solid generated by revolving the area enclosed between the evolute, 27ay^2 = 4(x-2a) ^3 and the parabola, y^2 = 4ax about x-axis.

Answer 1

$V=\int_a^{2a}(2 \sqrt{ax})dx$

$V=[2a^{0.5}*2a^{1.5}]_a^{2a}$

$V=\frac{2 \sqrt{a}}{3}*2*x|_a^{2a}$

$V=\frac{4 \sqrt{a}}{3}[(2a)^{1.5}-a^{1.5}]$

$V=\frac{4 \sqrt{a}}{3}[2\sqrt{2}*a\sqrt{a}-a\sqrt{a}]$

$V=\frac{4 a\sqrt{a}}{3}\sqrt{a}[2\sqrt{2}-1]$

$V=\frac{4 a^2}{3}[2\sqrt{2}-1]$