Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.

Correct result:

r =  1.3333 m
h =  1 m

Solution:

a=4 m v=3 m  s2=(a/2)2+v2 s=(a/2)2+v2=(4/2)2+32=13 m3.6056 m  (vh):r=v:a/2 v=h+r v:a/2 h=vr 2v/a  V=πr2 h V=πr2(vr 2v/a) V=πr2(vr 2v/a) V=πr2(3r 2 3/4) V=3/2π(avr)r V=0  3/2π (avr)r=0  3/2pi(43r)r=0  3/2 3.1415926 (43r)r=0 14.1371667r2+18.85r=0 14.1371667r218.85r=0  a=14.1371667;b=18.85;c=0 D=b24ac=18.852414.13716670=355.3057463175 D>0  r1,2=b±D2a=18.85±355.3128.2743334 r1,2=0.66666667±0.66666666666667 r1=1.3333333333333 r2=0   Factored form of the equation:  14.1371667(r1.3333333333333)r=0 r=r1=1.3333=43=1.3333 m

Our quadratic equation calculator calculates it.

h=vr 2 v/a=31.3333 2 3/4=1 m



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