# The trench

Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.

Correct result:

V =  48 m3

#### Solution:

$l=20 \ \text{m} \ \\ a=3 \ \text{m} \ \\ c=1.8 \ \text{m} \ \\ h=1 \ \text{m} \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 3+1.8 }{ 2 } \cdot \ 1=\dfrac{ 12 }{ 5 }=2.4 \ \text{m}^2 \ \\ \ \\ V=S \cdot \ l=2.4 \cdot \ 20=48 \ \text{m}^3$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

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.
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
• Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
• 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
• The funnel
The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
• Hexagonal pyramid
Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.
• 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.
• Fountain
The stone fountain, which has the shape of a cylinder with a diameter of 3 m, is 70 cm deep. How many m2 of stone is wetted with water?
• Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• Height
The content of the triangle is 35 cm2. The length of the base is 10 cm. Determine the length of the height on the base.