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.

Correct answer:

V =  37.3333 cm³
S =  74.2409 cm²

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ h=7\text{ cm } \\ {S}_1=a^2=4^2=16{\text{cm}}^2 \\ V=S_1\cdot h\mathrm{/}3=16\cdot 7\mathrm{/}3=37.3333{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} h_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{7^2+(4\mathrm{/}2{)}^2}=\sqrt{53}\text{ cm}\doteq 7.2801\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=4\cdot 7.2801\mathrm{/}2=2\sqrt{53}{\text{cm}}^2\doteq 14.5602{\text{cm}}^2 \\ S=S_1+4\cdot S_2=16+4\cdot 14.5602=74.2409{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• 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
• 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.
• 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.
• Hexagonal pyramid
  Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
• 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.
• Triangular pyramid
  Calculate the volume and surface area of a regular triangular pyramid with height equal to the base edge 10 cm length.
• Pyramid four sides
  In a regular tetrahedral pyramid is a body height of 38 cm and a wall height of 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
• Quadrangular pyramid
  Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
• 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.
• 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 =?
• Triangular pyramid
  Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
• Hexagonal pyramid
  Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
• 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.
• Quadrangular prism
  Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
• 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
• Hexagonal pyramid
  Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• Regular hexagonal pyramid
  Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.