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. Find the container's radius r (and height h) so that they can hide the largest possible treasure.

Correct answer:

r =  1.3333 m
h =  1 m

Step-by-step explanation:

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 14.137167r2+18.85r=0 14.137167r218.85r=0  a=14.137167;b=18.85;c=0 D=b24ac=18.852414.1371670=355.3057463175 D>0  r1,2=2ab±D=28.27433418.85±355.31 r1,2=0.66666665±0.66666665251956 r1=1.3333333050391 r2=0   Factored form of the equation:  14.137167(r1.3333333050391)r=0 r=r1=1.3333=1.3333 m

Our quadratic equation calculator calculates it.

h=vr 2 v/a=31.3333 2 3/4=1 m

Did you find an error or inaccuracy? Feel free to write us. Thank you!


Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: