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=$s^3/{πr^2r}=s^3/{πr^3}={1/π}*{(s/r)^3}={1/π}*{(π/3)}^{3/2}=π^{1/2}/3^{3/2}$

 


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