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Well the formula for the area of a trapezoid is as follows:
A=
where a and b are both base measures (a trapezoid has a top and bottom base).
Therefore, if all three have the same base length (the top and bottom lengths themselves being different yet the same on all three), the trapezoid with the greatest angle measure would have the greatest are. This is because with a greater angle measure comes a greater height (Pythagorean theorem).<span />
A=
where a and b are both base measures (a trapezoid has a top and bottom base).
Therefore, if all three have the same base length (the top and bottom lengths themselves being different yet the same on all three), the trapezoid with the greatest angle measure would have the greatest are. This is because with a greater angle measure comes a greater height (Pythagorean theorem).<span />
Answer:
V = 34,13*π cubic units
Step-by-step explanation: See Annex
We find the common points of the two curves, solving the system of equations:
y² = 2*x x = 2*y ⇒ y = x/2
(x/2)² = 2*x
x²/4 = 2*x
x = 2*4 x = 8 and y = 8/2 y = 4
Then point P ( 8 ; 4 )
The other point Q is Q ( 0; 0)
From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.
Now with the help of geogebra we have: In the annex segment ABCD is dy then
V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy
V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴
V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )
V = π * [256/3 - 51,20]
V = 34,13*π cubic units
