Truncated pyramid

How many cubic meters is the volume of a regular four-sided truncated pyramid with edges one meter and 60 cm and high 250 mm?

Correct answer:

V =  0.1633 m³

Step-by-step explanation:

$$\begin{gathered} a_1=1\text{ m } \\ {a}_2=60\mathrm{/}100={\displaystyle \frac{3}{5}}=0.6\text{ m } \\ h=250\mathrm{/}1000={\displaystyle \frac{1}{4}}=0.25\text{ m } \\ {S}_1=a_1^2=1^2=1{\text{m}}^2 \\ {S}_2=a_2^2=0.6^2={\displaystyle \frac{9}{25}}=0.36{\text{m}}^2 \\ V=h\mathrm{/}3\cdot (S_1+\sqrt{S_1\cdot S_2}+S_2)=0.25\mathrm{/}3\cdot (1+\sqrt{1\cdot 0.36}+0.36)=0.1633{\text{m}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Truncated pyramid
  The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
• Truncated pyramid
  Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees
• Rope
  How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
• Runcated pyramid teapot
  The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
• Tetrahedral pyramid
  Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
• 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.
• Cuboid - volume and areas
  The cuboid has a volume of 250 cm³, a surface of 250 cm², and one side 5 cm long. How do I calculate the remaining sides?
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Insulate house
  The property owner wants to insulate his house. The house has these dimensions 12, and 12 m is 15 m high. The windows have 6 with dimensions 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need?
• The coil
  How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
• Quadrangular pyramid
  Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =?
• The square
  The square oak board (with density ρ = 700 kg/m³) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
• Painter 3
  Dad want to paint wall high 250 cm wide and 230 cm with wallpaper. How many meters must buy wallpaper if wallpaper width is 60 cm?
• Pillar
  Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
• Painting
  The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents.
• Hexagon cut pyramid
  Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.