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:

Our quadratic equation calculator calculates it.

$h=v-r\cdot 2\cdot v\mathrm{/}a=3-1.3333\cdot 2\cdot 3\mathrm{/}4=1\text{ m}$

Try another example

Related math problems and questions:

• The tent
  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 tent
  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.
• Pyramid cut
  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
• Cylindrical container
  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.
• Quadrilateral pyramid
  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
• Quadrilateral pyramid
  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.
• Tent
  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.
• Distance of points
  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
  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
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if the edge of the base is 8 cm long and the height of the side wall is 5 cm?
• The 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.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Triangular pyramid
  What is the volume of a regular triangular pyramid with a side 3 cm long?
• Iglu - cone tent
  The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring), if 20% needs to be added to the minimum amount due to cutting waste? b
• Top of the tower
  The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• Tetrahedral pyramid
  What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
• The quadrilateral pyramid
  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.