Prism

Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.

Correct result:

S =  203.84 cm²
V =  139.2 cm³

Solution:

$$\begin{gathered} v=10 \\ a=5.8 \\ b=3 \\ w=2.4 \\ o=2\cdot (a+b)=2\cdot (5.8+3)={\displaystyle \frac{88}{5}}=17.6 \\ {S}_1=a\cdot w=5.8\cdot 2.4={\displaystyle \frac{348}{25}}=13.92 \\ S=2\cdot S_1+o\cdot v=2\cdot 13.92+17.6\cdot 10={\displaystyle \frac{5096}{25}}={\displaystyle \frac{5096}{25}}{\text{cm}}^2=203.84{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot v=13.92\cdot 10={\displaystyle \frac{696}{5}}={\displaystyle \frac{696}{5}}{\text{cm}}^3=139.2{\text{cm}}^3$

Try another example

Showing 0 comments:

Next similar math problems:

• Triangular prism
  Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
• Tetrahedral prism
  Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
• Prism 4 sides
  Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig
• Triangular prism
  Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm.
• Square prism
  Calculate the volume of a square prism of high 2 dm wherein the base is: rectangle with sides 17 cm and 1.3 dm
• Surface area
  Calculate the surface area of a four-sides 2-m high prism which base is a rectangle with sides 17 cm and 1.3 dm
• 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.
• Juice box
  The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
• 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.
• Triangular prism
  Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm, and height of prism h=12 cm.
• Regular prism
  The regular four-sided prism has a base of 25 cm² and a surface of 210 cm². Find its volume.
• Square prism
  Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
• Triangular prism
  The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The content area of the largest sidewall of its surface is 130 cm², and the height of the body is 10 cm. Calculate its volume.
• 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.
• Trapezoidal prism
  Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm. L
• Hexagonal prism
  Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm.