Surface area + triangle - math problems

Number of problems found: 195

School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm ^ 3
Right-angled triangle base
Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
How to
How to find a total surface of a rectangular pyramid if each face is to be 8 dm high and the base is 10 dm by 6 dm.
Frustrum - volume, area
Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.
Axial section
Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm.
The tetrahedron
Calculate the surface area and volume of a regular tetrahedron 4.9 cm high, the base edge has a length of 6 cm.
Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
The roof
The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste
Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
Surface and volume - cube
Find the surface and volume of a cube whose wall diagonal is 5 cm long.
Triangular prism
The regular triangular prism has a base edge of 8.6 dm and a height of 1.5 m. Finf its volume and surface area.
The rotating
The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
The volume
The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.
Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
A spherical segment
A spherical section whose axial section has an angle of j = 120° in the center of the sphere is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
Truncated cone
Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.
Regular 4-sided pyramid
Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.
Hexaprism container
Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m with a base edge of 3dm and a corresponding height of 2.6 dm.