Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.

Result

V =  10 cm3
S =  25.605 cm2

Solution:

V=1/3 (5 4/2) 3=10 cm3V=1/3 \cdot \ (5 \cdot \ 4/2) \cdot \ 3 = 10 \ cm^3
S=5 4/2+3 4/2+52+42 3/2=25.605 cm2S=5 \cdot \ 4/2+ 3 \cdot \ 4/2 + \sqrt{ 5^{ 2 }+4^{ 2 } } \cdot \ 3/2 = 25.605 \ cm^2







Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




See also our trigonometric triangle calculator. Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Cheops pyramid
    Pyramid-cheops The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It made from limestone with a density of 2.7 g/cm3. Calculate the amount of stone in tons. How many trains with 30 twenty tons wagons carry the stone?
  2. Secret treasure
    max_cylinder_pyramid 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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  3. Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  4. Rectangular cuboid
    cuboid_1 The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
  5. The cuboid
    nadrz The cuboid is filled to the brim with water. The external dimensions are 95 cm, 120 cm, and 60 cm. The thickness of all walls and the bottom is 5 cm. How many liters of water fit into the cuboid?
  6. 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 larges
  7. TV transmitter
    praded The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
  8. Space diagonal
    cube_diagonals The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
  9. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
  10. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
  11. A concrete pedestal
    frustum-of-a-right-circular-cone A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
  12. The cylinder 2
    cylinder Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
  13. The hemisphere
    naklon_koule The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
  14. Floating of wood - Archimedes law
    balza05 What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m3 that floats in alcohol? (alcohol density is 789 kg/m3)
  15. Frustum of a cone
    cone-frustrum A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
  16. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?
  17. Three glasses
    skleniceRGB Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the b