This is the cross section of the cone of solid X.
The top bit is INSIDE the hemisphere. So I am only interested in the bottom smaller cone.
Volume of little cone:
$$\\=\frac{1}{3}\pi r^2 h\\\\
=\frac{1}{3}\pi* 25* 15\\\\
=\frac{1}{3}\pi* 25* 15\\\\
=75\pi\\\\$$
Volume of hemisphere
$$\\=\frac{1}{2}*\frac{4}{3} \pi r^3\\\\
=\frac{4}{6}\pi* 9^3\\\\
=\frac{2}{3}\pi* 9^3\\\\
=486 \pi$$
total volume of solid X = $$486\pi + 75\pi = 561 \pi\;\;cm^3$$
Now the ratio of surface areas of X:Y = 25:36
so the ratio of lengths of X:Y = 5:6
and the ratio of volumes X:Y = 125: 216
$$\\\frac{216}{125}=\frac{Y}{561\pi}\\\\
\frac{216}{125}\times 561\pi=Y\\\\
Y=\frac{216}{125}\times 561\pi\\\\
Volume\;of\;Y=\frac{121176\pi}{125}\;\;cm^3\\\\$$
This is the cross section of the cone of solid X.
The top bit is INSIDE the hemisphere. So I am only interested in the bottom smaller cone.
Volume of little cone:
$$\\=\frac{1}{3}\pi r^2 h\\\\
=\frac{1}{3}\pi* 25* 15\\\\
=\frac{1}{3}\pi* 25* 15\\\\
=75\pi\\\\$$
Volume of hemisphere
$$\\=\frac{1}{2}*\frac{4}{3} \pi r^3\\\\
=\frac{4}{6}\pi* 9^3\\\\
=\frac{2}{3}\pi* 9^3\\\\
=486 \pi$$
total volume of solid X = $$486\pi + 75\pi = 561 \pi\;\;cm^3$$
Now the ratio of surface areas of X:Y = 25:36
so the ratio of lengths of X:Y = 5:6
and the ratio of volumes X:Y = 125: 216
$$\\\frac{216}{125}=\frac{Y}{561\pi}\\\\
\frac{216}{125}\times 561\pi=Y\\\\
Y=\frac{216}{125}\times 561\pi\\\\
Volume\;of\;Y=\frac{121176\pi}{125}\;\;cm^3\\\\$$