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 14.1371667r2+18.85r=0 14.1371667r218.85r=0  a=14.1371667;b=18.85;c=0 D=b24ac=18.852414.13716670=355.305746317 D>0  r1,2=b±D2a=18.85±355.3128.2743334 r1,2=0.66666667±0.666666666667 r1=1.33333333333 r2=0   Factored form of the equation:  14.1371667(r1.33333333333)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



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




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:

  • The tent
    stan Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.
  • Quadrilateral pyramid
    jehlan_2 A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
  • Cylindrical container
    valec2_6 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  • Triangular pyramid
    TriangularPyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
  • The tent
    stan The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
  • The quadrilateral pyramid
    jehlan_4b_obdelnik The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
  • Tent
    stan Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
  • Alien ship
    cube_in_sphere The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
  • Regular 4-sided pyramid
    jehlan Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.
  • Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  • Distance of points
    jehlan_4b_obdelnik_1 A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
  • Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  • Find the
    ihlan Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm3 and a height of 45 cm.
  • Quadrilateral pyramid
    jehlan_1 We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
  • Quadrilateral pyramid
    jehlan3 In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
  • The pyramid
    pyramid The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid.
  • 4side pyramid
    ihlany Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.