Quadrangular prism

Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.

Correct answer:

V =  8470 cm³
S =  2661.8889 cm²

Step-by-step explanation:

$$\begin{gathered} u=22\text{ cm } \\ a=u\mathrm{/}\sqrt{2}=22\mathrm{/}\sqrt{2}=11\sqrt{2}\text{ cm}\doteq 15.5563\text{ cm } \\ {S}_1=a^2=15.5563^2=242{\text{cm}}^2 \\ h=35\text{ cm } \\ V=S_1\cdot h=242\cdot 35=8470{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=4\cdot a\cdot h=4\cdot 15.5563\cdot 35\doteq 2177.8889{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 242+2177.8889=2661.8889{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• 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.
• 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 =?
• 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.
• Regular hexagonal prism
  Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Quadrilateral prism
  Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
• Rhombus base
  Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 15 cm. Prism height is twice the base edge length.
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.
• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Body diagonal - cube
  Calculate the surface and cube volume with body diagonal 15 cm long.
• Triangular prism
  The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
• Body 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
• Triangular prism - regular
  The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
• Find the
  Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm³ and a height of 45 cm.