#1**+5 **

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\\\\$$

Melody
Feb 16, 2015

#1**+5 **

Best Answer

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\\\\$$

Melody
Feb 16, 2015