23. Solids
Some formulas to be memorized (there is no getting around this):
```1. Euler's Formula for Solids: \$F+V=E+2\$,
where F = Number of Faces,
V = Number of Vertices &
E = Number of Edges

2. Cube of side s: Volume=\$s^3\$, Surface Area =\$6s^2\$

3. Sphere of radius r: Volume=\$4/3πr^3\$, Surface Area=\$4πr^2\$

4. Cylinder with base radius r and height h: Volume=\$πr^2h\$, Surface Area=2πrh (curved part)+\$2πr^2\$(either end)

5. Cone with base radius r and height h: Volume=\$1/3πr^2h\$, Surface Area=\$πrl\$ where \$l^2=r^2+h^2\$
```

e.g. A cube of side s has the same surface area as the curved surface area of a cylinder of radius and height r. The ratio of their volumes is?
The question tells us, \$6s^2=2πr^2\$, so \$s/r=√{π/3}\$. Ratio of volumes=\$s^3/{πr^2r}=s^3/{πr^3}={1/π}*{(s/r)^3}={1/π}*{(π/3)}^{3/2}=π^{1/2}/3^{3/2}\$

 Follow @xChiPrime Tweet

By continuing to use this website, you acknowledge that this service is provided as is, with no warranty of any kind whatsoever.
Copyright 2015 ChiPrime. All rights reserved.