Find the

Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm³ and a height of 45 cm.

Correct answer:

S =  5539.5431 cm²

Step-by-step explanation:

$$\begin{gathered} V=24{\text{dm}}^3\to {\text{cm}}^3=24\cdot 1000{\text{cm}}^3=24000{\text{cm}}^3 \\ h=45\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h \\ {S}_1=3\cdot V\mathrm{/}h=3\cdot 24000\mathrm{/}45=1600{\text{cm}}^2 \\ {S}_1=a^2 \\ a=\sqrt{S_1}=\sqrt{1600}=40\text{ cm } \\ (a\mathrm{/}2{)}^2+h^2=h_2^2 \\ {h}_2=\sqrt{(a\mathrm{/}2{)}^2+h^2}=\sqrt{(40\mathrm{/}2{)}^2+45^2}=5\sqrt{97}\text{ cm}\doteq 49.2443\text{ cm } \\ {S}_2={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{40\cdot 49.2443}{2}}=100\sqrt{97}{\text{cm}}^2\doteq 984.8858{\text{cm}}^2 \\ S=4\cdot S_2+S_1=4\cdot 984.8858+1600=5539.5431{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• The regular
  The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.
• 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
• 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.
• 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.
• 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?
• Regular 4-sided pyramid
  Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m.
• 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.
• Quadrilateral pyramid
  Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
• 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
• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, and its height is 120 cm. What is the surface area of the cone?
• 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.
• 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
• 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.
• 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.
• Pyramid a+h
  Calculate the pyramid's volume and surface area with the edge and height a = 26 cm. h = 3 dm.
• 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.