Question

An theatrical company makes a pyramid for a stage production. The pyramid has a square base with sides 1,2 m.the top of the pyramid is 2m above the base. How many liters of paint are needed to cover the outside of the pyramid, if 750 ml is used for every 2m^2 ,and if the base is not painted?
A)3,34
B)1,88
C18,79
D)3,20
E)6.68

Answer 1

Let's assume that the pyramid is $SABCD$ where $ABCD$ is the base square and $O$ is the center of the $ABCD$ (i.e. $O=AC\cap BD$ ).

Let $M$ be the middle of $AB$ ($M\in AB$ ,$AM=MB=\frac12 AB$ ).

Given $OS=2$ and $AB=1.2$ we have to find $0.750/2\cdot (4S_{ABS})$ .

Now we find:

1. $OM$

2. $MS$

3. $S_{ABS}=\frac12 ah=\frac12 AB\cdot MS$

4. and produce the answer.

$OM=\frac12 AB=0.6$ ; from $\Delta OSM$ , $\angle MOS=90^\circ$ , $MS=\sqrt{OM^2+OS^2}=\sqrt{4.36}$

$S_{ABS}=\frac12 AB\cdot MS=0.6\sqrt{4.36}$ .

The answer is $0.750/2\cdot (4S_{ABS})=0.750/2\cdot (4\cdot 0.6\sqrt{4.36})=0.9\sqrt{4.36}\approx 1.8792551716038992\approx 1.88$ so the right answer is B.