Can anyone help me with this technical maths question, including formulas, how its done ect,?

Question

What are the formulas, how have you done that to get that awnswer. Thanks.
I need hellp, please help, I have a test tommorow based on question like these. Thanks

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Answer 1

2)
a pipe D= 50 mm
S = 3,14159 X 50 X 50 / 4
S = 1963,5 mm²

Vol = S X L [1 m = 1000 mm]
Vol = 1963500 mm³ or 1,96 liters

This is the volume for the pipe / but we need to calculate the volume of liquid for a section with 40 mm height.

Imagine a circle, D = 50 and r = 25 mm

There is a triangle O (center) A B divided in 2 triangles:
O A X and O B X (X is the point in the segment A B - in the midle)

O X = 15 mm (radius = 25 mm and there is 10 mm empty in the pipe)

Make a draw => XA = XB = 20 mm
OX = 15 mm

The angle XOB = arc tg 20/15 = 53,13 º
The angle AOB = 106,26º

Sector AOB area (surface) = Pi * D ^ 4 = 1963,5 mm² / 360 º * 106,26 º = 579,6 mm²

Surface area of triangle AOB = 40 mm * 15 mm /2 = 300 mm ²

Then the empty area = 579,6 mm² - 300 mm² = 279,6 mm²

The empty volume of 1 m of pipe is 279600 mm³ = 0,28 liters

ANSWER = 1,96 liters - 0,28 liters = 1,68 liters