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

Correct answer:

S =  14.4 dm²
m =  2.56 kg

Step-by-step explanation:

$$\begin{gathered} a=20\text{ cm } \\ h=24\text{ cm } \\ {S}_1=a^2=20^2=400{\text{cm}}^2 \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{24^2+(20\mathrm{/}2{)}^2}=26\text{ cm } \\ {S}_2={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{20\cdot 26}{2}}=260{\text{cm}}^2 \\ {S}_3=S_1+4\cdot S_2=400+4\cdot 260=1440{\text{cm}}^2 \\ S=S_3\to {\text{dm}}^2=S_3\mathrm{/}100{\text{dm}}^2=1440\mathrm{/}100{\text{dm}}^2=14.4{\text{dm}}^2={\displaystyle \frac{72}{5}}{\text{dm}}^2 \end{gathered}$$

$$\begin{gathered} \rho =0.8{\text{g/cm}}^3 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 400\cdot 24=3200{\text{cm}}^3 \\ {m}_1=V\cdot \rho =3200\cdot 0.8=2560\text{ g } \\ m=m_1\to \text{ kg}=m_1\mathrm{/}1000\text{ kg}=2560\mathrm{/}1000\text{ kg}=2.56\text{ kg}={\displaystyle \frac{64}{25}}\text{ kg} \end{gathered}$$

Try another example

Related math problems and questions:

• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
• Regular quadrilateral pyramid
  Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
• Tetrahedral pyramid
  Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm², and the deviation angle of the side edges from the plane of the base is 60 degrees.
• 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?
• Quadrilateral pyramid
  We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
• 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.
• 4side pyramid
  Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
• Pyramid 4sides
  Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
• 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.
• Find the
  Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm³ and a height of 45 cm.
• 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.
• The regular
  The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.
• Quadrilateral pyramid
  Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.
• Tetrahedral pyramid
  A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
• 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
• 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.
• Quadrangular pyramid
  The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.