Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.

Correct answer:

V =  0.3183 m³
S =  3.5744 m²

Step-by-step explanation:

$$\begin{gathered} a=7\text{ dm}\to \text{ m}=7\mathrm{/}10\text{ m}=0.7\text{ m } \\ h=1.5\text{ m } \\ P={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 0.7^2\doteq 0.2122{\text{m}}^2 \\ V=P\cdot h=0.2122\cdot 1.5=0.3183{\text{m}}^3 \end{gathered}$$

$S=2\cdot P+3\cdot a\cdot h=2\cdot 0.2122+3\cdot 0.7\cdot 1.5=3.5744{\text{m}}^2$

Try another example

Related math problems and questions:

• Prism
  Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
• 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.
• Triangular prism
  The regular triangular prism has a base edge of 8.6 dm and a height of 1.5 m. Finf its volume and surface area.
• Right-angled triangle base
  Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
• Prism
  Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
• Diagonals of a prism
  The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
• Surface and volume
  Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
• Triangular prism
  Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)
• Prism - eq triangle
  Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
• Tent
  Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
• Prism
  The volume of tetrahedral prism is 2.43 m³. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
• 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
• Hexaprism container
  Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m with a base edge of 3dm and a corresponding height of 2.6 dm.
• Hexagonal prism
  The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
• The regular
  The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• 3sides prism
  The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
• Rotating cone
  Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.