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.

Correct answer:

V =  1064 cm³
S =  754 cm²

Step-by-step explanation:

$$\begin{gathered} a_1=17\text{ cm } \\ {a}_2=5\text{ cm } \\ v=8\text{ cm } \\ {S}_1=a_1^2=17^2=289{\text{cm}}^2 \\ {S}_2=a_2^2=5^2=25{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot v\cdot (S_1+\sqrt{S_1\cdot S_2}+S_2)={\displaystyle \frac{1}{3}}\cdot 8\cdot (289+\sqrt{289\cdot 25}+25)=1064{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} h_2=\sqrt{v^2+((a_1-a_2)\mathrm{/}2{)}^2}=\sqrt{8^2+((17-5)\mathrm{/}2{)}^2}=10\text{ cm } \\ {S}_3={\displaystyle \frac{a_1+a_2}{2}}\cdot h_2={\displaystyle \frac{17+5}{2}}\cdot 10=110{\text{cm}}^2 \\ S=S_1+S_2+4\cdot S_3=289+25+4\cdot 110=754{\text{cm}}^2 \end{gathered}$$

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.
• 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
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 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.
• Truncated pyramid
  The truncated regular quadrilateral pyramid has a volume of 74 cm³, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base.
• 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
  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
• 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.
• 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.
• 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.
• 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
• 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.
• 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.
• Triangular pyramid
  It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (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.
• The regular
  The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.