# 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:

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.

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.

#### You need to know the following knowledge to solve this word math problem:

**geometry**- similarity of triangles
**algebra**- quadratic equation
- equation
- expression of a variable from the formula
**arithmetic**- square root
- square (second power, quadratic)
**solid geometry**- cylinder
- pyramid
**planimetrics**- Pythagorean theorem
- right triangle
- triangle
**basic functions**- maximum
- minimum
- derivation
**units**- volume
- high school

## 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 m^{2}of cloth we need to make the tent if we have to add 7% of the seams? How many m^{3}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 cm^{2}. Find the area of the - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3}. 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 dm^{3}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 cm^{2}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 m^{2}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.